Burman, Erik; Delay, Guillaume; Ern, Alexandre; Oksanen, Lauri A stability estimate for data assimilation subject to the heat equation with initial datum. (Une estimée de stabilité pour l’assimilation de données pour l’équation de la chaleur avec une donnée initiale.) (English. French summary) Zbl 07811816 C. R., Math., Acad. Sci. Paris 361, 1521-1530 (2023). MSC: 35B60 35A23 35B30 35K05 35K20 PDFBibTeX XMLCite \textit{E. Burman} et al., C. R., Math., Acad. Sci. Paris 361, 1521--1530 (2023; Zbl 07811816) Full Text: DOI
Steins, Morgane; Ern, Alexandre; Jamond, Olivier; Drui, Florence Time-explicit hybrid high-order method for the nonlinear acoustic wave equation. (English) Zbl 07787602 ESAIM, Math. Model. Numer. Anal. 57, No. 5, 2977-3006 (2023). Reviewer: Petr Sváček (Praha) MSC: 65M60 65M06 65N30 65M22 35L05 76Q05 74J30 65F10 65F08 65F05 PDFBibTeX XMLCite \textit{M. Steins} et al., ESAIM, Math. Model. Numer. Anal. 57, No. 5, 2977--3006 (2023; Zbl 07787602) Full Text: DOI
Ern, Alexandre; Guermond, Jean-Luc The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct. (English) Zbl 1528.65069 SIAM J. Numer. Anal. 61, No. 6, 2940-2966 (2023). MSC: 65M60 65M06 65N30 65M12 78A25 35L02 35L05 35Q61 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, SIAM J. Numer. Anal. 61, No. 6, 2940--2966 (2023; Zbl 1528.65069) Full Text: DOI
Burman, Erik; Delay, Guillaume; Ern, Alexandre The unique continuation problem for the heat equation discretized with a high-order space-time nonconforming method. (English) Zbl 07764838 SIAM J. Numer. Anal. 61, No. 5, 2534-2557 (2023). MSC: 65M30 65M60 65J20 35R25 35K05 PDFBibTeX XMLCite \textit{E. Burman} et al., SIAM J. Numer. Anal. 61, No. 5, 2534--2557 (2023; Zbl 07764838) Full Text: DOI
Niakh, Idrissa; Drouet, Guillaume; Ehrlacher, Virginie; Ern, Alexandre Stable model reduction for linear variational inequalities with parameter-dependent constraints. (English) Zbl 1515.65299 ESAIM, Math. Model. Numer. Anal. 57, No. 1, 167-189 (2023). MSC: 65N30 65N12 65N22 35A23 35A01 35A02 49M41 74M15 74S05 PDFBibTeX XMLCite \textit{I. Niakh} et al., ESAIM, Math. Model. Numer. Anal. 57, No. 1, 167--189 (2023; Zbl 1515.65299) Full Text: DOI
Ern, Alexandre; Hédin, Florent; Pichot, Géraldine; Pignet, Nicolas Hybrid high-order methods for flow simulations in extremely large discrete fracture networks. (English) Zbl 1512.65265 SMAI J. Comput. Math. 8, 375-398 (2022). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N50 65F35 76S05 76U60 86A05 35R02 PDFBibTeX XMLCite \textit{A. Ern} et al., SMAI J. Comput. Math. 8, 375--398 (2022; Zbl 1512.65265) Full Text: DOI
Ern, Alexandre; Guermond, Jean-Luc Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and \(H^{1+r}, r>0\), regularity. (English) Zbl 1501.35156 Found. Comput. Math. 22, No. 5, 1273-1308 (2022). MSC: 35J25 65N15 65N30 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, Found. Comput. Math. 22, No. 5, 1273--1308 (2022; Zbl 1501.35156) Full Text: DOI arXiv
Ern, Alexandre; Guermond, Jean-Luc Invariant-domain-preserving high-order time stepping. I: Explicit Runge-Kutta schemes. (English) Zbl 1501.65070 SIAM J. Sci. Comput. 44, No. 5, A3366-A3392 (2022). Reviewer: Bülent Karasözen (Ankara) MSC: 65M60 65L06 65M06 65N30 35L65 65M12 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, SIAM J. Sci. Comput. 44, No. 5, A3366--A3392 (2022; Zbl 1501.65070) Full Text: DOI
Burman, Erik; Duran, Omar; Ern, Alexandre Hybrid high-order methods for the acoustic wave equation in the time domain. (English) Zbl 1499.65483 Commun. Appl. Math. Comput. 4, No. 2, 597-633 (2022). MSC: 65M60 65M22 65M12 65N30 35L05 65L06 76Q05 PDFBibTeX XMLCite \textit{E. Burman} et al., Commun. Appl. Math. Comput. 4, No. 2, 597--633 (2022; Zbl 1499.65483) Full Text: DOI HAL
Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal \(hp\) approximation estimates in \(\boldsymbol{H}(\operatorname{div})\). (English) Zbl 1517.65108 IMA J. Numer. Anal. 42, No. 2, 1023-1049 (2022). MSC: 65N30 65N50 65N15 65N12 35B65 35B45 PDFBibTeX XMLCite \textit{A. Ern} et al., IMA J. Numer. Anal. 42, No. 2, 1023--1049 (2022; Zbl 1517.65108) Full Text: DOI arXiv
Burman, Erik; Duran, Omar; Ern, Alexandre Unfitted hybrid high-order methods for the wave equation. (English) Zbl 1507.65202 Comput. Methods Appl. Mech. Eng. 389, Article ID 114366, 23 p. (2022). MSC: 65M99 35L05 PDFBibTeX XMLCite \textit{E. Burman} et al., Comput. Methods Appl. Mech. Eng. 389, Article ID 114366, 23 p. (2022; Zbl 1507.65202) Full Text: DOI HAL
Carstensen, Carsten; Ern, Alexandre; Puttkammer, Sophie Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method. (English) Zbl 1502.65179 Numer. Math. 149, No. 2, 273-304 (2021). MSC: 65N25 65N30 65N12 35P15 15A18 35J05 PDFBibTeX XMLCite \textit{C. Carstensen} et al., Numer. Math. 149, No. 2, 273--304 (2021; Zbl 1502.65179) Full Text: DOI
Burman, Erik; Delay, Guillaume; Ern, Alexandre A hybridized high-order method for unique continuation subject to the Helmholtz equation. (English) Zbl 1481.65207 SIAM J. Numer. Anal. 59, No. 5, 2368-2392 (2021). MSC: 65N20 65N30 65J20 65N12 65N15 35R25 35J05 PDFBibTeX XMLCite \textit{E. Burman} et al., SIAM J. Numer. Anal. 59, No. 5, 2368--2392 (2021; Zbl 1481.65207) Full Text: DOI
Ern, Alexndre; Vohralík, Martin; Zakerzadeh, Mohammad Guaranteed and robust \(L^2 \)-norm a posteriori error estimates for 1D linear advection problems. (English) Zbl 1490.65270 ESAIM, Math. Model. Numer. Anal. 55, Suppl., 447-474 (2021). MSC: 65N30 35F05 65N15 PDFBibTeX XMLCite \textit{A. Ern} et al., ESAIM, Math. Model. Numer. Anal. 55, 447--474 (2021; Zbl 1490.65270) Full Text: DOI arXiv
Lusso, Christelle; Bouchut, François; Ern, Alexandre; Mangeney, Anne Explicit solutions to a free interface model for the static/flowing transition in thin granular flows. (English) Zbl 1481.35340 ESAIM, Math. Model. Numer. Anal. 55, Suppl., 369-395 (2021). Reviewer: Roberta Bianchini (Roma) MSC: 35Q35 76A10 76T25 35R35 74N20 PDFBibTeX XMLCite \textit{C. Lusso} et al., ESAIM, Math. Model. Numer. Anal. 55, 369--395 (2021; Zbl 1481.35340) Full Text: DOI Link
Chaumont-Frelet, T.; Ern, A.; Vohralík, M. On the derivation of guaranteed and \(p\)-robust a posteriori error estimates for the Helmholtz equation. (English) Zbl 1500.65096 Numer. Math. 148, No. 3, 525-573 (2021). Reviewer: Wei Gong (Beijing) MSC: 65N30 65N15 65N50 35J05 PDFBibTeX XMLCite \textit{T. Chaumont-Frelet} et al., Numer. Math. 148, No. 3, 525--573 (2021; Zbl 1500.65096) Full Text: DOI arXiv
Burman, Erik; Duran, Omar; Ern, Alexandre; Steins, Morgane Convergence analysis of hybrid high-order methods for the wave equation. (English) Zbl 1480.65248 J. Sci. Comput. 87, No. 3, Paper No. 91, 30 p. (2021). Reviewer: Temur A. Jangveladze (Tbilisi) MSC: 65M60 65M06 65N30 65M12 65M15 65L06 74J10 74S05 35Q74 PDFBibTeX XMLCite \textit{E. Burman} et al., J. Sci. Comput. 87, No. 3, Paper No. 91, 30 p. (2021; Zbl 1480.65248) Full Text: DOI HAL
Burman, Erik; Cicuttin, Matteo; Delay, Guillaume; Ern, Alexandre An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. (English) Zbl 1475.65186 SIAM J. Sci. Comput. 43, No. 2, A859-A882 (2021). Reviewer: Vit Dolejsi (Praha) MSC: 65N30 65N15 65N12 65N85 35J05 PDFBibTeX XMLCite \textit{E. Burman} et al., SIAM J. Sci. Comput. 43, No. 2, A859--A882 (2021; Zbl 1475.65186) Full Text: DOI
Ern, Alexandre; Guermond, Jean-Luc Finite elements III. First-order and time-dependent PDEs. (English) Zbl 1457.65001 Texts in Applied Mathematics 74. Cham: Springer (ISBN 978-3-030-57347-8/hbk; 978-3-030-57349-2/pbk; 978-3-030-57348-5/ebook). viii, 417 p. (2021). MSC: 65-01 35-01 65N30 65M60 35Qxx PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, Finite elements III. First-order and time-dependent PDEs. Cham: Springer (2021; Zbl 1457.65001) Full Text: DOI
Ern, Alexandre; Guermond, Jean-Luc Finite elements II. Galerkin approximation, elliptic and mixed PDEs. (English) Zbl 1476.65002 Texts in Applied Mathematics 73. Cham: Springer (ISBN 978-3-030-56922-8/hbk; 978-3-030-56924-2/pbk; 978-3-030-56923-5/ebook). ix, 492 p. (2021). MSC: 65-01 35-01 65N30 65M60 35Jxx 35Mxx PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, Finite elements II. Galerkin approximation, elliptic and mixed PDEs. Cham: Springer (2021; Zbl 1476.65002) Full Text: DOI
Chaumont-Frelet, Théophile; Ern, Alexandre; Vohralík, Martin Polynomial-degree-robust \(\boldsymbol H(\mathbf{curl})\)-stability of discrete minimization in a tetrahedron. (English. French summary) Zbl 1456.65156 C. R., Math., Acad. Sci. Paris 358, No. 9-10, 1101-1110 (2020). MSC: 65N30 65K10 65N15 35J05 78M10 35Q60 46E35 PDFBibTeX XMLCite \textit{T. Chaumont-Frelet} et al., C. R., Math., Acad. Sci. Paris 358, No. 9--10, 1101--1110 (2020; Zbl 1456.65156) Full Text: DOI arXiv
Cicuttin, Matteo; Ern, Alexandre; Gudi, Thirupathi Hybrid high-order methods for the elliptic obstacle problem. (English) Zbl 1436.65176 J. Sci. Comput. 83, No. 1, Paper No. 8, 18 p. (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65N30 65N15 65N12 35B45 PDFBibTeX XMLCite \textit{M. Cicuttin} et al., J. Sci. Comput. 83, No. 1, Paper No. 8, 18 p. (2020; Zbl 1436.65176) Full Text: DOI HAL
Boiveau, Thomas; Ehrlacher, Virginie; Ern, Alexandre; Nouy, Anthony Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. (English) Zbl 1422.65250 ESAIM, Math. Model. Numer. Anal. 53, No. 2, 635-658 (2019). MSC: 65M60 65M12 65M22 35K20 65N30 65F10 65F30 PDFBibTeX XMLCite \textit{T. Boiveau} et al., ESAIM, Math. Model. Numer. Anal. 53, No. 2, 635--658 (2019; Zbl 1422.65250) Full Text: DOI arXiv
Calo, Victor; Cicuttin, Matteo; Deng, Quanling; Ern, Alexandre Spectral approximation of elliptic operators by the hybrid high-order method. (English) Zbl 1422.65359 Math. Comput. 88, No. 318, 1559-1586 (2019). Reviewer: Pavel Burda (Praha) MSC: 65N25 65N30 35J25 65N15 35P15 PDFBibTeX XMLCite \textit{V. Calo} et al., Math. Comput. 88, No. 318, 1559--1586 (2019; Zbl 1422.65359) Full Text: DOI arXiv
Cicuttin, Matteo; Ern, Alexandre; Lemaire, Simon On the implementation of a multiscale hybrid high-order method. (English) Zbl 1456.65158 Radu, Florin Adrian (ed.) et al., Numerical mathematics and advanced applications. ENUMATH 2017. Selected papers based on the presentations at the European conference, Bergen, Norway, September 25–29, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 126, 509-517 (2018). MSC: 65N30 65N50 65N08 35J15 PDFBibTeX XMLCite \textit{M. Cicuttin} et al., Lect. Notes Comput. Sci. Eng. 126, 509--517 (2018; Zbl 1456.65158) Full Text: DOI HAL
Burman, Erik; Ern, Alexandre A cut cell hybrid high-order method for elliptic problems with curved boundaries. (English) Zbl 1427.65350 Radu, Florin Adrian (ed.) et al., Numerical mathematics and advanced applications. ENUMATH 2017. Selected papers based on the presentations at the European conference, Bergen, Norway, September 25–29, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 126, 173-181 (2018). MSC: 65N30 65N50 35J25 65N85 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, Lect. Notes Comput. Sci. Eng. 126, 173--181 (2018; Zbl 1427.65350) Full Text: DOI HAL
Daniel, Patrik; Ern, Alexandre; Smears, Iain; Vohralík, Martin An adaptive \(hp\)-refinement strategy with computable guaranteed bound on the error reduction factor. (English) Zbl 1427.65356 Comput. Math. Appl. 76, No. 5, 967-983 (2018). MSC: 65N30 65N12 65N50 65N15 35J05 PDFBibTeX XMLCite \textit{P. Daniel} et al., Comput. Math. Appl. 76, No. 5, 967--983 (2018; Zbl 1427.65356) Full Text: DOI arXiv
Cascavita, Karol L.; Bleyer, Jérémy; Chateau, Xavier; Ern, Alexandre Hybrid discretization methods with adaptive yield surface detection for Bingham pipe flows. (English) Zbl 1407.65141 J. Sci. Comput. 77, No. 3, 1424-1443 (2018). MSC: 65M08 65M06 65M50 35Q35 76A05 PDFBibTeX XMLCite \textit{K. L. Cascavita} et al., J. Sci. Comput. 77, No. 3, 1424--1443 (2018; Zbl 1407.65141) Full Text: DOI HAL
Ern, Alexandre; Guermond, Jean-Luc Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell’s equations. (English) Zbl 1401.65132 Comput. Methods Appl. Math. 18, No. 3, 451-475 (2018). MSC: 65N30 65N12 76R50 35Q61 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, Comput. Methods Appl. Math. 18, No. 3, 451--475 (2018; Zbl 1401.65132) Full Text: DOI HAL
Benaceur, Amina; Ehrlacher, Virginie; Ern, Alexandre; Meunier, Sébastien A progressive reduced basis/empirical interpolation method for nonlinear parabolic problems. (English) Zbl 1397.65180 SIAM J. Sci. Comput. 40, No. 5, A2930-A2955 (2018). MSC: 65M60 65D05 80M10 80A20 35K55 35K05 PDFBibTeX XMLCite \textit{A. Benaceur} et al., SIAM J. Sci. Comput. 40, No. 5, A2930--A2955 (2018; Zbl 1397.65180) Full Text: DOI arXiv
Burman, Erik; Ern, Alexandre An unfitted hybrid high-order method for elliptic interface problems. (English) Zbl 1448.65201 SIAM J. Numer. Anal. 56, No. 3, 1525-1546 (2018). MSC: 65N15 65N30 35J15 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, SIAM J. Numer. Anal. 56, No. 3, 1525--1546 (2018; Zbl 1448.65201) Full Text: DOI arXiv
Ern, Alexandre; Smears, Iain; VohralÍk, Martin Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. (English) Zbl 1378.65165 SIAM J. Numer. Anal. 55, No. 6, 2811-2834 (2017). MSC: 65M15 65M60 35K20 PDFBibTeX XMLCite \textit{A. Ern} et al., SIAM J. Numer. Anal. 55, No. 6, 2811--2834 (2017; Zbl 1378.65165) Full Text: DOI arXiv
Ern, Alexandre; Smears, Iain; Vohralík, Martin Discrete \(p\)-robust \(\boldsymbol H(\mathrm{div})\)-liftings and a posteriori estimates for elliptic problems with \(H^{-1}\) source terms. (English) Zbl 1378.65173 Calcolo 54, No. 3, 1009-1025 (2017). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65N15 35J25 PDFBibTeX XMLCite \textit{A. Ern} et al., Calcolo 54, No. 3, 1009--1025 (2017; Zbl 1378.65173) Full Text: DOI arXiv
Cantin, Pierre; Bonelle, Jérôme; Burman, Erik; Ern, Alexandre A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization. (English) Zbl 1368.65248 Comput. Math. Appl. 72, No. 9, 2057-2071 (2016). MSC: 65N50 65N12 35F15 PDFBibTeX XMLCite \textit{P. Cantin} et al., Comput. Math. Appl. 72, No. 9, 2057--2071 (2016; Zbl 1368.65248) Full Text: DOI
Di Pietro, Daniele A.; Ern, Alexandre; Lemaire, Simon A review of hybrid high-order methods: formulations, computational aspects, comparison with other methods. (English) Zbl 1357.65258 Barrenechea, Gabriel R. (ed.) et al., Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Selected papers based on the presentations at the 101st LMS-EPSRC symposium, Durham, UK, July 8–16, 2014. Cham: Springer (ISBN 978-3-319-41638-0/hbk; 978-3-319-41640-3/ebook). Lecture Notes in Computational Science and Engineering 114, 205-236 (2016). MSC: 65N30 35J25 65N12 65N15 PDFBibTeX XMLCite \textit{D. A. Di Pietro} et al., Lect. Notes Comput. Sci. Eng. 114, 205--236 (2016; Zbl 1357.65258) Full Text: DOI HAL
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin \(hp\)-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. (English) Zbl 1351.65082 SIAM J. Sci. Comput. 38, No. 5, A3220-A3246 (2016). MSC: 65N15 35J25 35J05 65N30 65N12 65N50 PDFBibTeX XMLCite \textit{V. Dolejší} et al., SIAM J. Sci. Comput. 38, No. 5, A3220--A3246 (2016; Zbl 1351.65082) Full Text: DOI
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. (English) Zbl 1341.65045 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 635-650 (2016). MSC: 65N30 35J25 65N08 65N15 PDFBibTeX XMLCite \textit{B. Cockburn} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 3, 635--650 (2016; Zbl 1341.65045) Full Text: DOI HAL
Beirão da Veiga, L. (ed.); Ern, A. (ed.) Preface. (English) Zbl 1349.00239 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 633-634 (2016). MSC: 00B15 65-06 35-06 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} (ed.) and \textit{A. Ern} (ed.), ESAIM, Math. Model. Numer. Anal. 50, No. 3, 633--634 (2016; Zbl 1349.00239) Full Text: DOI
Cantin, Pierre; Ern, Alexandre Vertex-based compatible discrete operator schemes on polyhedral meshes for advection-diffusion equations. (English) Zbl 1336.65184 Comput. Methods Appl. Math. 16, No. 2, 187-212 (2016). MSC: 65N22 65N12 65N15 35J25 65N50 PDFBibTeX XMLCite \textit{P. Cantin} and \textit{A. Ern}, Comput. Methods Appl. Math. 16, No. 2, 187--212 (2016; Zbl 1336.65184) Full Text: DOI HAL
Bonelle, Jérôme; Di Pietro, Daniele A.; Ern, Alexandre Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes. (English) Zbl 1417.65197 Comput. Aided Geom. Des. 35-36, 27-41 (2015). MSC: 65N30 65N12 35J25 PDFBibTeX XMLCite \textit{J. Bonelle} et al., Comput. Aided Geom. Des. 35--36, 27--41 (2015; Zbl 1417.65197) Full Text: DOI HAL
Di Pietro, Daniele A.; Ern, Alexandre Hybrid high-order methods for variable-diffusion problems on general meshes. (Méthodes hybrides d’ordre élevé pour des problèmes à diffusion variable sur des maillages généraux.) (English. French summary) Zbl 1308.65196 C. R., Math., Acad. Sci. Paris 353, No. 1, 31-34 (2015). MSC: 65N30 35J05 65N12 65N15 PDFBibTeX XMLCite \textit{D. A. Di Pietro} and \textit{A. Ern}, C. R., Math., Acad. Sci. Paris 353, No. 1, 31--34 (2015; Zbl 1308.65196) Full Text: DOI HAL
Casenave, Fabien; Ern, Alexandre; Sylvand, Guillaume Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain. (English) Zbl 1349.76184 J. Comput. Phys. 257, Part A, 627-644 (2014). MSC: 76M10 76M15 65N30 35J05 65N38 76Q05 PDFBibTeX XMLCite \textit{F. Casenave} et al., J. Comput. Phys. 257, Part A, 627--644 (2014; Zbl 1349.76184) Full Text: DOI arXiv
Bonelle, Jérôme; Ern, Alexandre Analysis of compatible discrete operator schemes for elliptic problems on polyhedral meshes. (English) Zbl 1297.65132 ESAIM, Math. Model. Numer. Anal. 48, No. 2, 553-581 (2014). Reviewer: Abdallah Bradji (Annaba) MSC: 65N12 65N08 65N30 35J25 PDFBibTeX XMLCite \textit{J. Bonelle} and \textit{A. Ern}, ESAIM, Math. Model. Numer. Anal. 48, No. 2, 553--581 (2014; Zbl 1297.65132) Full Text: DOI arXiv
Casenave, Fabien; Ern, Alexandre; Lelièvre, Tony Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method. (English) Zbl 1288.65157 ESAIM, Math. Model. Numer. Anal. 48, No. 1, 207-229 (2014). MSC: 65N15 65N38 35J05 76Q05 76M15 PDFBibTeX XMLCite \textit{F. Casenave} et al., ESAIM, Math. Model. Numer. Anal. 48, No. 1, 207--229 (2014; Zbl 1288.65157) Full Text: DOI arXiv
Ern, Alexandre; Guermond, Jean-Luc Weighting the edge stabilization. (English) Zbl 1280.65095 SIAM J. Numer. Anal. 51, No. 3, 1655-1677 (2013). Reviewer: Charis Harley (Johannesburg) MSC: 65M12 35L65 65M60 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, SIAM J. Numer. Anal. 51, No. 3, 1655--1677 (2013; Zbl 1280.65095) Full Text: DOI Link
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. (English) Zbl 1278.65138 SIAM J. Numer. Anal. 51, No. 2, 773-793 (2013). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M15 65M50 35K65 65M06 65M60 PDFBibTeX XMLCite \textit{V. Dolejší} et al., SIAM J. Numer. Anal. 51, No. 2, 773--793 (2013; Zbl 1278.65138) Full Text: DOI HAL
Ern, Alexandre; Vohralík, Martin Four closely related equilibrated flux reconstructions for nonconforming finite elements. (English. French summary) Zbl 1261.65117 C. R., Math., Acad. Sci. Paris 351, No. 1-2, 77-80 (2013). MSC: 65N30 35J05 65N50 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, C. R., Math., Acad. Sci. Paris 351, No. 1--2, 77--80 (2013; Zbl 1261.65117) Full Text: DOI HAL
Burman, Erik; Ern, Alexandre Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. (English) Zbl 1281.65123 ESAIM, Math. Model. Numer. Anal. 46, No. 4, 681-707 (2012). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M20 65L06 65M15 65M60 65M12 35K20 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, ESAIM, Math. Model. Numer. Anal. 46, No. 4, 681--707 (2012; Zbl 1281.65123) Full Text: DOI
Tryoen, J.; Le Maître, O.; Ern, A. Adaptive anisotropic spectral stochastic methods for uncertain scalar conservation laws. (English) Zbl 1273.35330 SIAM J. Sci. Comput. 34, No. 5, A2459-A2481 (2012). Reviewer: Dominique Lepingle (Orléans) MSC: 35R60 60H35 35L65 PDFBibTeX XMLCite \textit{J. Tryoen} et al., SIAM J. Sci. Comput. 34, No. 5, A2459--A2481 (2012; Zbl 1273.35330) Full Text: DOI
Di Pietro, Daniele A.; Ern, Alexandre Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions. (English) Zbl 1267.65178 Numer. Methods Partial Differ. Equations 28, No. 4, 1161-1177 (2012). Reviewer: Gisbert Stoyan (Budapest) MSC: 65N30 35R05 65N12 65N15 35J25 PDFBibTeX XMLCite \textit{D. A. Di Pietro} and \textit{A. Ern}, Numer. Methods Partial Differ. Equations 28, No. 4, 1161--1177 (2012; Zbl 1267.65178) Full Text: DOI HAL
Ern, Alexandre; Joubaud, Rémi; Lelièvre, Tony Mathematical study of non-ideal electrostatic correlations in equilibrium electrolytes. (English) Zbl 1245.35125 Nonlinearity 25, No. 6, 1635-1652 (2012). MSC: 35Q70 35J66 82B21 49J35 49K35 49K20 PDFBibTeX XMLCite \textit{A. Ern} et al., Nonlinearity 25, No. 6, 1635--1652 (2012; Zbl 1245.35125) Full Text: DOI Link
Di Pietro, Daniele Antonio; Ern, Alexandre Mathematical aspects of discontinuous Galerkin methods. (English) Zbl 1231.65209 Mathématiques & Applications (Berlin) 69. Berlin: Springer (ISBN 978-3-642-22979-4/pbk; 978-3-642-22980-0/ebook). xvii, 384 p. (2012). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65M60 76M10 65-02 76R50 76M12 76D05 35Q30 65N12 65M12 65N50 65M50 PDFBibTeX XMLCite \textit{D. A. Di Pietro} and \textit{A. Ern}, Mathematical aspects of discontinuous Galerkin methods. Berlin: Springer (2012; Zbl 1231.65209) Full Text: DOI
Burman, Erik; Ern, Alexandre; Fernández, Miguel A. Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems. (English) Zbl 1226.65086 SIAM J. Numer. Anal. 48, No. 6, 2019-2042 (2010). Reviewer: Yajuan Sun (Beijing) MSC: 65M60 65M12 65M15 65L06 35F46 PDFBibTeX XMLCite \textit{E. Burman} et al., SIAM J. Numer. Anal. 48, No. 6, 2019--2042 (2010; Zbl 1226.65086) Full Text: DOI
Ern, Alexandre; Vohralík, Martin A posteriori error estimation based on potential and flux reconstruction for the heat equation. (English) Zbl 1215.65152 SIAM J. Numer. Anal. 48, No. 1, 198-223 (2010). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M15 65M60 65M06 35K05 65M08 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, SIAM J. Numer. Anal. 48, No. 1, 198--223 (2010; Zbl 1215.65152) Full Text: DOI
Perotto, Simona; Ern, Alexandre; Veneziani, Alessandro Hierarchical local model reduction for elliptic problems: A domain decomposition approach. (English) Zbl 1206.65251 Multiscale Model. Simul. 8, No. 4, 1102-1127 (2010). MSC: 65N55 65N30 35J25 PDFBibTeX XMLCite \textit{S. Perotto} et al., Multiscale Model. Simul. 8, No. 4, 1102--1127 (2010; Zbl 1206.65251) Full Text: DOI HAL
Tryoen, J.; Le Maître, O.; Ndjinga, M.; Ern, A. Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. (English) Zbl 1197.65013 J. Comput. Phys. 229, No. 18, 6485-6511 (2010). MSC: 65C30 60H15 60H35 35R60 35L05 65M60 65M70 PDFBibTeX XMLCite \textit{J. Tryoen} et al., J. Comput. Phys. 229, No. 18, 6485--6511 (2010; Zbl 1197.65013) Full Text: DOI HAL
Di Pietro, Daniele A.; Ern, Alexandre Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations. (English) Zbl 1369.76024 Math. Comput. 79, No. 271, 1303-1330 (2010). MSC: 76M10 76D05 65N30 35Q30 46E39 46N20 65N12 PDFBibTeX XMLCite \textit{D. A. Di Pietro} and \textit{A. Ern}, Math. Comput. 79, No. 271, 1303--1330 (2010; Zbl 1369.76024) Full Text: DOI
Ern, Alexandre; Stephansen, Annette F.; Vohralík, Martin Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. (English) Zbl 1190.65165 J. Comput. Appl. Math. 234, No. 1, 114-130 (2010). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N15 65N30 76S05 35J25 35B25 PDFBibTeX XMLCite \textit{A. Ern} et al., J. Comput. Appl. Math. 234, No. 1, 114--130 (2010; Zbl 1190.65165) Full Text: DOI
Chazel, F.; Benoit, M.; Ern, A.; Piperno, S. A double-layer Boussinesq-type model for highly nonlinear and dispersive waves. (English) Zbl 1186.35156 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2108, 2319-2346 (2009). MSC: 35Q35 76B15 PDFBibTeX XMLCite \textit{F. Chazel} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2108, 2319--2346 (2009; Zbl 1186.35156) Full Text: DOI arXiv Link
Ern, Alexandre; Stephansen, Annette F.; Zunino, Paolo A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity. (English) Zbl 1165.65074 IMA J. Numer. Anal. 29, No. 2, 235-256 (2009). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N12 65N15 35J25 PDFBibTeX XMLCite \textit{A. Ern} et al., IMA J. Numer. Anal. 29, No. 2, 235--256 (2009; Zbl 1165.65074) Full Text: DOI Link
Ern, Alexandre; Vohralík, Martin Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. (English) Zbl 1161.65085 C. R., Math., Acad. Sci. Paris 347, No. 7-8, 441-444 (2009). MSC: 65N30 35J25 65N15 65N50 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, C. R., Math., Acad. Sci. Paris 347, No. 7--8, 441--444 (2009; Zbl 1161.65085) Full Text: DOI
Di Pietro, Daniele A.; Ern, Alexandre A discontinuous Galerkin flux for anisotropic heterogeneous second-order elliptic problems. (English) Zbl 1422.65382 Eymard, Robert (ed.) et al., Finite volumes for complex applications. V. Proceedings of the 5th International Symposium, Aussois, June 2008. London: ISTE. 777-793 (2008). MSC: 65N30 35Jxx PDFBibTeX XMLCite \textit{D. A. Di Pietro} and \textit{A. Ern}, in: Finite volumes for complex applications. V. Proceedings of the 5th International Symposium, Aussois, June 2008. London: ISTE. 777--793 (2008; Zbl 1422.65382)
Di Pietro, Daniele A.; Ern, Alexandre; Guermond, Jean-Luc Discontinuous Galerkin methods for anisotropic semidefinite diffusion with advection. (English) Zbl 1165.49032 SIAM J. Numer. Anal. 46, No. 2, 805-831 (2008). Reviewer: Jan Lovíšek (Bratislava) MSC: 49M15 49K40 65N30 35J25 35R05 65N12 65N15 PDFBibTeX XMLCite \textit{D. A. Di Pietro} et al., SIAM J. Numer. Anal. 46, No. 2, 805--831 (2008; Zbl 1165.49032) Full Text: DOI Link
Ern, Alexandre; Guermond, Jean-Luc Discontinuous Galerkin methods for Friedrichs’ systems. Part III. Multifield theories with partial coercivity. (English) Zbl 1179.65145 SIAM J. Numer. Anal. 46, No. 2, 776-804 (2008). Reviewer: Georg Hebermehl (Berlin) MSC: 65N30 65M60 35F15 35Q35 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, SIAM J. Numer. Anal. 46, No. 2, 776--804 (2008; Zbl 1179.65145) Full Text: DOI Link
Ern, Alexandre; Stephansen, Annette F. A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods. (English) Zbl 1174.65034 J. Comput. Math. 26, No. 4, 488-510 (2008). MSC: 65M15 65M60 35K57 PDFBibTeX XMLCite \textit{A. Ern} and \textit{A. F. Stephansen}, J. Comput. Math. 26, No. 4, 488--510 (2008; Zbl 1174.65034)
Ern, A.; Perotto, S.; Veneziani, A. Hierarchical model reduction for advection-diffusion-reaction problems. (English) Zbl 1157.65487 Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 703-710 (2008). MSC: 65N30 35J25 65N15 PDFBibTeX XMLCite \textit{A. Ern} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10--14, 2007. Berlin: Springer. 703--710 (2008; Zbl 1157.65487)
Achchab, Boujemaâ; El Fatini, Mohamed; Ern, Alexandre; Souissi, A. Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport. (English) Zbl 1154.65080 C. R., Math., Acad. Sci. Paris 346, No. 21-22, 1187-1190 (2008). MSC: 65N15 35J25 65N12 65N30 PDFBibTeX XMLCite \textit{B. Achchab} et al., C. R., Math., Acad. Sci. Paris 346, No. 21--22, 1187--1190 (2008; Zbl 1154.65080) Full Text: DOI
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin An accurate \(\mathbf H\)(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. (English) Zbl 1129.65085 C. R., Math., Acad. Sci. Paris 345, No. 12, 709-712 (2007). MSC: 65N30 35J25 65N15 PDFBibTeX XMLCite \textit{A. Ern} et al., C. R., Math., Acad. Sci. Paris 345, No. 12, 709--712 (2007; Zbl 1129.65085) Full Text: DOI
Burman, Erik; Ern, Alexandre A continuous finite element method with face penalty to approximate Friedrichs’ systems. (English) Zbl 1129.65083 ESAIM, Math. Model. Numer. Anal. 41, No. 1, 55-76 (2007). Reviewer: Petr Necesal (Plzen) MSC: 65N30 65N12 74S05 35F15 74F10 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, ESAIM, Math. Model. Numer. Anal. 41, No. 1, 55--76 (2007; Zbl 1129.65083) Full Text: DOI Numdam EuDML
Ern, Alexandre; Guermond, Jean-Luc; Caplain, Gilbert An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrich’ systems. (An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrichs’ systems.) (English) Zbl 1118.47003 Commun. Partial Differ. Equations 32, No. 2, 317-341 (2007). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 47A05 46C05 35F05 35F15 47F05 47N20 PDFBibTeX XMLCite \textit{A. Ern} et al., Commun. Partial Differ. Equations 32, No. 2, 317--341 (2007; Zbl 1118.47003) Full Text: DOI
Burman, Erik; Ern, Alexandre Continuous interior penalty \(hp\)-finite element methods for advection and advection-diffusion equations. (English) Zbl 1118.65118 Math. Comput. 76, No. 259, 1119-1140 (2007). Reviewer: Willy Govaerts (Gent) MSC: 65N30 65N12 65N15 35J25 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, Math. Comput. 76, No. 259, 1119--1140 (2007; Zbl 1118.65118) Full Text: DOI
El Alaoui, L.; Ern, A.; Burman, E. A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations. (English) Zbl 1112.65109 IMA J. Numer. Anal. 27, No. 1, 151-171 (2007). Reviewer: Isaac Yevzerov (Kyïv) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{L. El Alaoui} et al., IMA J. Numer. Anal. 27, No. 1, 151--171 (2007; Zbl 1112.65109) Full Text: DOI Link
Ern, Alexandre; Guermond, Jean-Luc Discontinuous Galerkin methods for Friedrichs’ systems. II: Second-order elliptic PDEs. (English) Zbl 1133.65098 SIAM J. Numer. Anal. 44, No. 6, 2363-2388 (2006). Reviewer: Georg Hebermehl (Berlin) MSC: 65N30 65N12 35F15 35J05 76W05 76M10 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, SIAM J. Numer. Anal. 44, No. 6, 2363--2388 (2006; Zbl 1133.65098) Full Text: DOI
El Alaoui, L.; Ern, A.; Burman, E. A nonconforming finite element method with face penalty for advection-diffusion equations. (English) Zbl 1119.65407 Bermúdez de Castro, Alfredo (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18–22, 2005. Berlin: Springer (ISBN 3-540-34287-7/hbk). 512-519 (2006). MSC: 65N30 35J25 65N15 PDFBibTeX XMLCite \textit{L. El Alaoui} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18--22, 2005. Berlin: Springer. 512--519 (2006; Zbl 1119.65407)
Burman, Erik; Ern, Alexandre Continuous interior penalty \(hp\)-finite element methods for transport operators. (English) Zbl 1119.65406 Bermúdez de Castro, Alfredo (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18–22, 2005. Berlin: Springer (ISBN 3-540-34287-7/hbk). 504-511 (2006). MSC: 65N30 35J25 65N15 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18--22, 2005. Berlin: Springer. 504--511 (2006; Zbl 1119.65406)
Ern, Alexandre; Guermond, Jean-Luc Discontinuous Galerkin methods for Friedrichs’ systems. (English) Zbl 1119.65408 Bermúdez de Castro, Alfredo (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18–22, 2005. Berlin: Springer (ISBN 3-540-34287-7/hbk). 79-96 (2006). MSC: 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18--22, 2005. Berlin: Springer. 79--96 (2006; Zbl 1119.65408)
Ern, Alexandre; Proft, Jennifer Multi-algorithmic methods for coupled hyperbolic-parabolic problems. (English) Zbl 1111.35131 Int. J. Numer. Anal. Model. 3, No. 1, 94-114 (2006). Reviewer: Temuri A. Jangveladze (Tbilisi) MSC: 35R35 65N30 35M10 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J. Proft}, Int. J. Numer. Anal. Model. 3, No. 1, 94--114 (2006; Zbl 1111.35131)
El Alaoui, Linda; Ern, Alexandre Nonconforming finite element methods with subgrid viscosity applied to advection-diffusion-reaction equations. (English) Zbl 1104.65110 Numer. Methods Partial Differ. Equations 22, No. 5, 1106-1126 (2006). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{L. El Alaoui} and \textit{A. Ern}, Numer. Methods Partial Differ. Equations 22, No. 5, 1106--1126 (2006; Zbl 1104.65110) Full Text: DOI
Ern, Alexandre; Guermond, Jean-Luc Evaluation of the condition number in linear systems arising in finite element approximations. (English) Zbl 1149.65306 ESAIM, Math. Model. Numer. Anal. 40, No. 1, 29-48 (2006). MSC: 65F35 65F10 65N30 35J25 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, ESAIM, Math. Model. Numer. Anal. 40, No. 1, 29--48 (2006; Zbl 1149.65306) Full Text: DOI Numdam EuDML
Ern, A.; Guermond, J.-L. Discontinuous Galerkin methods for Friedrichs’ systems. I: General theory. (English) Zbl 1122.65111 SIAM J. Numer. Anal. 44, No. 2, 753-778 (2006). Reviewer: Georg Hebermehl (Berlin) MSC: 65N30 65N12 35J25 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J. L. Guermond}, SIAM J. Numer. Anal. 44, No. 2, 753--778 (2006; Zbl 1122.65111) Full Text: DOI Link
Croisille, J.-P.; Ern, A.; Lelièvre, T.; Proft, J. Analysis and simulation of a coupled hyperbolic/parabolic model problem. (English) Zbl 1081.65084 J. Numer. Math. 13, No. 2, 81-103 (2005). Reviewer: Vit Dolejsi (Praha) MSC: 65M06 47D06 76M12 65M60 35M20 35M10 PDFBibTeX XMLCite \textit{J. P. Croisille} et al., J. Numer. Math. 13, No. 2, 81--103 (2005; Zbl 1081.65084) Full Text: DOI
Burman, Erik; Ern, Alexandre Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence. (English) Zbl 1078.65088 Math. Comput. 74, No. 252, 1637-1652 (2005). Reviewer: Emil Minchev (Tokyo) MSC: 65N12 65N30 35J25 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, Math. Comput. 74, No. 252, 1637--1652 (2005; Zbl 1078.65088) Full Text: DOI
Ern, Alexandre; Proft, Jennifer A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. (English) Zbl 1084.65092 Appl. Math. Lett. 18, No. 7, 833-841 (2005). Reviewer: Michal Beneš (Praha) MSC: 65M60 35K15 65N15 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J. Proft}, Appl. Math. Lett. 18, No. 7, 833--841 (2005; Zbl 1084.65092) Full Text: DOI
El Alaoui, Linda; Ern, Alexandre Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods. (English) Zbl 1077.65113 M2AN, Math. Model. Numer. Anal. 38, No. 6, 903-929 (2004). Reviewer: Karel Najzar (Praha) MSC: 65N15 65N30 35J25 76M10 76M12 76S05 PDFBibTeX XMLCite \textit{L. El Alaoui} and \textit{A. Ern}, M2AN, Math. Model. Numer. Anal. 38, No. 6, 903--929 (2004; Zbl 1077.65113) Full Text: DOI Numdam EuDML
Ern, Alexandre; Guermond, Jean-Luc Theory and practice of finite elements. (English) Zbl 1059.65103 Applied Mathematical Sciences 159. New York, NY: Springer (ISBN 0-387-20574-8/hbk). xiii, 524 p. (2004). Reviewer: I. N. Katz (St. Louis) MSC: 65N30 65N50 35A35 65F10 65M60 74S05 76D07 35J25 35K15 35Q30 65-02 76M10 65Y05 65M15 65N12 65M12 78M10 80M10 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, Theory and practice of finite elements. New York, NY: Springer (2004; Zbl 1059.65103)
Burman, Erik; Ern, Alexandre Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes. (English. Abridged French version) Zbl 1049.65128 C. R., Math., Acad. Sci. Paris 338, No. 8, 641-646 (2004). MSC: 65N30 65N12 65N15 35J05 35J25 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, C. R., Math., Acad. Sci. Paris 338, No. 8, 641--646 (2004; Zbl 1049.65128) Full Text: DOI Link
Bongiovanni, Emmanuel; Ern, Alexandre; Glinsky-Olivier, Nathalie A new relaxation method for the compressible Navier-Stokes equations. (English) Zbl 1137.76417 Math. Models Methods Appl. Sci. 13, No. 10, 1379-1396 (2003). MSC: 76M12 76N10 65M12 35Q35 PDFBibTeX XMLCite \textit{E. Bongiovanni} et al., Math. Models Methods Appl. Sci. 13, No. 10, 1379--1396 (2003; Zbl 1137.76417) Full Text: DOI
Braack, Malte; Ern, Alexandre A posteriori control of modeling errors and discretization errors. (English) Zbl 1050.65100 Multiscale Model. Simul. 1, No. 2, 221-238 (2003). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65N15 65N30 65N50 80M10 35B27 80A20 PDFBibTeX XMLCite \textit{M. Braack} and \textit{A. Ern}, Multiscale Model. Simul. 1, No. 2, 221--238 (2003; Zbl 1050.65100) Full Text: DOI
Burman, E.; Ern, A. The discrete maximum principle for stabilized finite element methods. (English) Zbl 1043.65113 Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer (ISBN 88-470-0180-3/hbk). 557-566 (2003). MSC: 65M60 65M12 35K15 PDFBibTeX XMLCite \textit{E. Burman} and \textit{A. Ern}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer. 557--566 (2003; Zbl 1043.65113) Full Text: DOI
Bongiovanni, Emmanuel; Ern, Alexandre; Glinsky-Olivier, Nathalie A new relaxation method for the compressible Navier-Stokes equations. (Une nouvelle méthode de relaxation pour les équations de Navier-Stokes compressibles.) (French. Abridged English version) Zbl 1068.76057 C. R., Math., Acad. Sci. Paris 336, No. 3, 283-288 (2003). MSC: 76M12 76N10 65M12 35Q35 PDFBibTeX XMLCite \textit{E. Bongiovanni} et al., C. R., Math., Acad. Sci. Paris 336, No. 3, 283--288 (2003; Zbl 1068.76057) Full Text: DOI
Bongiovanni, E.; Ern, A.; Glinsky-Olivier, N. A new relaxation method for the compressible Navier-Stokes equations. (English) Zbl 1173.76357 Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24–28, 2002. London: Hermes Penton Science (ISBN 1-9039-9634-1/pbk). 293-300 (2002). MSC: 76M12 76N10 65M12 35Q35 PDFBibTeX XMLCite \textit{E. Bongiovanni} et al., in: Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24--28, 2002. London: Hermes Penton Science. 293--300 (2002; Zbl 1173.76357)
Ern, Alexandre; Guermond, Jean-Luc Éléments finis: théorie, applications, mise en œuvre. (Finite elements: Theory, applications, implementation.) (French) Zbl 0993.65123 Mathématiques & Applications (Berlin) 36. Berlin: Springer. ix, 430 p. EUR 71.04 (net); sFr 118.00; £49.50; $ 79.95 (2002). Reviewer: Michel Bernadou (Paris La Defense) MSC: 65N30 65M50 65N50 65Y05 65N15 65M15 65N12 65M12 65F10 78M10 80M10 35J25 35K15 35Q30 65-02 76M10 74S05 65M60 76D07 PDFBibTeX XMLCite \textit{A. Ern} and \textit{J.-L. Guermond}, Finite elements: Theory, applications, implementation. Berlin: Springer (2002; Zbl 0993.65123)
Ern, A.; Guermond, J.-J.; Quartapelle, L. Vorticity-velocity formulations of the Stokes problem in 3D. (English) Zbl 0939.35144 Math. Methods Appl. Sci. 22, No. 6, 531-546 (1999). Reviewer: K.Deckelnick (Brighton) MSC: 35Q30 35A15 35D05 76D07 PDFBibTeX XMLCite \textit{A. Ern} et al., Math. Methods Appl. Sci. 22, No. 6, 531--546 (1999; Zbl 0939.35144) Full Text: DOI
Ern, Alexandre Vorticity-velocity formulation of the Stokes problem with variable density and viscosity. (English) Zbl 0953.76079 Math. Models Methods Appl. Sci. 8, No. 2, 203-218 (1998). Reviewer: A.R.Rao (Bangalore) MSC: 76N10 35Q30 PDFBibTeX XMLCite \textit{A. Ern}, Math. Models Methods Appl. Sci. 8, No. 2, 203--218 (1998; Zbl 0953.76079) Full Text: DOI
Ern, Alexandre Vorticity-velocity formulation of the Stokes problem with variable density and viscosity. (English. Abridged French version) Zbl 0865.76082 C. R. Acad. Sci., Paris, Sér. I 323, No. 10, 1159-1164 (1996). MSC: 76N10 35Q30 PDFBibTeX XMLCite \textit{A. Ern}, C. R. Acad. Sci., Paris, Sér. I 323, No. 10, 1159--1164 (1996; Zbl 0865.76082)
Ern, Alexandre Vorticity-velocity formulation of the Navier-Stokes equations with variable density and viscosity. (Sur la formulation tourbillon-vitesse des équations de Navier-Stokes avec densité et viscosité variables.) (French. Abridged English version) Zbl 0923.76262 C. R. Acad. Sci., Paris, Sér. II, Fasc. b 323, No. 12, 813-818 (1996). MSC: 76N10 35Q30 PDFBibTeX XMLCite \textit{A. Ern}, C. R. Acad. Sci., Paris, Sér. II, Fasc. b 323, No. 12, 813--818 (1996; Zbl 0923.76262)
Douglas, Craig C.; Ern, Alexandre; Smooke, Mitchell D. Numerical simulation of laminar diffusion flames. (English) Zbl 0900.65371 Astfalk, Greg (ed.), Applications on advanced architecture computers. Philadelphia, PA: SIAM. Software - Environments - Tools. 243-254 (1996). MSC: 65Z05 65Y05 80A25 35Q72 PDFBibTeX XMLCite \textit{C. C. Douglas} et al., in: Applications on advanced architecture computers. Philadelphia, PA: SIAM. 243--254 (1996; Zbl 0900.65371)
Ern, Alexandre; Giovangigli, Vincent; Keyes, David E.; Smooke, Mitchell D. Towards polyalgorithmic linear system solvers for nonlinear elliptic problems. (English) Zbl 0807.65027 SIAM J. Sci. Comput. 15, No. 3, 681-703 (1994). Reviewer: Z.Dostál (Ostrava) MSC: 65F10 65F35 65H10 65Y20 35J65 65N22 80A32 PDFBibTeX XMLCite \textit{A. Ern} et al., SIAM J. Sci. Comput. 15, No. 3, 681--703 (1994; Zbl 0807.65027) Full Text: DOI Link