Beilina, Larisa; Ghaderi Aram, Morteza; Karchevskii, Evgenii M. An adaptive finite element method for solving 3D electromagnetic volume integral equation with applications in microwave thermometry. (English) Zbl 07525120 J. Comput. Phys. 459, Article ID 111122, 21 p. (2022). MSC: 65Nxx 65Mxx 65Rxx PDFBibTeX XMLCite \textit{L. Beilina} et al., J. Comput. Phys. 459, Article ID 111122, 21 p. (2022; Zbl 07525120) Full Text: DOI
Dargaville, S.; Smedley-Stevenson, R. P.; Smith, P. N.; Pain, C. C. Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects. (English) Zbl 07508370 J. Comput. Phys. 421, Article ID 109759, 19 p. (2020). MSC: 85-XX 82-XX PDFBibTeX XMLCite \textit{S. Dargaville} et al., J. Comput. Phys. 421, Article ID 109759, 19 p. (2020; Zbl 07508370) Full Text: DOI arXiv
Bonilla, Jesús; Badia, Santiago Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems. (English) Zbl 1437.65134 J. Comput. Phys. 416, Article ID 109522, 22 p. (2020). MSC: 65M60 35L65 76M10 65M50 PDFBibTeX XMLCite \textit{J. Bonilla} and \textit{S. Badia}, J. Comput. Phys. 416, Article ID 109522, 22 p. (2020; Zbl 1437.65134) Full Text: DOI arXiv
Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. Numerical methods for conservation laws with rough flux. (English) Zbl 1437.35485 Stoch. Partial Differ. Equ., Anal. Comput. 8, No. 1, 186-261 (2020). MSC: 35L65 35A35 65M06 60H15 65C30 PDFBibTeX XMLCite \textit{H. Hoel} et al., Stoch. Partial Differ. Equ., Anal. Comput. 8, No. 1, 186--261 (2020; Zbl 1437.35485) Full Text: DOI arXiv
Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs. (English) Zbl 1440.65184 Comput. Methods Appl. Mech. Eng. 345, 951-982 (2019). MSC: 65N30 35R60 65N15 65N50 PDFBibTeX XMLCite \textit{A. Bespalov} et al., Comput. Methods Appl. Mech. Eng. 345, 951--982 (2019; Zbl 1440.65184) Full Text: DOI arXiv
Beckers, Susanne; Behrens, Jörn; Wollner, Winnifried Duality based error estimation in the presence of discontinuities. (English) Zbl 1422.65369 Appl. Numer. Math. 144, 83-99 (2019). MSC: 65N30 65N15 65M20 65M70 65M06 35L05 PDFBibTeX XMLCite \textit{S. Beckers} et al., Appl. Numer. Math. 144, 83--99 (2019; Zbl 1422.65369) Full Text: DOI
Beilina, Larisa; Hosseinzadegan, Samar An adaptive finite element method in reconstruction of coefficients in Maxwell’s equations from limited observations. (English) Zbl 1413.65363 Appl. Math., Praha 61, No. 3, 253-286 (2016). MSC: 65M60 65M06 65N30 65M22 65M32 65J20 PDFBibTeX XMLCite \textit{L. Beilina} and \textit{S. Hosseinzadegan}, Appl. Math., Praha 61, No. 3, 253--286 (2016; Zbl 1413.65363) Full Text: DOI arXiv Link
Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer G. An abstract analysis of optimal goal-oriented adaptivity. (English) Zbl 1382.65392 SIAM J. Numer. Anal. 54, No. 3, 1423-1448 (2016). MSC: 65N30 65N50 65Y20 PDFBibTeX XMLCite \textit{M. Feischl} et al., SIAM J. Numer. Anal. 54, No. 3, 1423--1448 (2016; Zbl 1382.65392) Full Text: DOI arXiv
Rostamy, D.; Qasemi, S. Discontinuous Petrov-Galerkin and Bernstein-Legendre polynomials method for solving fractional damped heat- and wave-like equations. (English) Zbl 07499223 J. Comput. Theor. Transp. 44, No. 1, 1-23 (2015). MSC: 82-XX PDFBibTeX XMLCite \textit{D. Rostamy} and \textit{S. Qasemi}, J. Comput. Theor. Transp. 44, No. 1, 1--23 (2015; Zbl 07499223) Full Text: DOI
Baccouch, Mahboub Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation. (English) Zbl 1332.65134 Numer. Methods Partial Differ. Equations 31, No. 5, 1461-1491 (2015). Reviewer: Marius Ghergu (Dublin) MSC: 65M15 35L05 65M20 65M12 65M60 PDFBibTeX XMLCite \textit{M. Baccouch}, Numer. Methods Partial Differ. Equations 31, No. 5, 1461--1491 (2015; Zbl 1332.65134) Full Text: DOI
Burman, Erik Error estimates for forward Euler shock capturing finite element approximations of the one-dimensional Burgers’ equation. (English) Zbl 1327.76092 Math. Models Methods Appl. Sci. 25, No. 11, Article ID 2015, 2015-2042 (2015). MSC: 76M10 65M12 65M15 65M60 PDFBibTeX XMLCite \textit{E. Burman}, Math. Models Methods Appl. Sci. 25, No. 11, Article ID 2015, 2015--2042 (2015; Zbl 1327.76092) Full Text: DOI arXiv
Bürg, Markus; Nazarov, Murtazo Goal-oriented adaptive finite element methods for elliptic problems revisited. (English) Zbl 1316.65098 J. Comput. Appl. Math. 287, 125-147 (2015). MSC: 65N30 65N12 65N15 65N50 35J05 PDFBibTeX XMLCite \textit{M. Bürg} and \textit{M. Nazarov}, J. Comput. Appl. Math. 287, 125--147 (2015; Zbl 1316.65098) Full Text: DOI
Malmberg, John Bondestam A posteriori error estimate in the Lagrangian setting for an inverse problem based on a new formulation of Maxwell’s system. (English) Zbl 1319.78014 Beilina, Larisa (ed.), Inverse problems and applications. Selected papers based on the presentations at the third annual workshop on inverse problems, Stockholm, Sweden, May 2–6, 2013. Cham: Springer (ISBN 978-3-319-12498-8/hbk; 978-3-319-12499-5/ebook). Springer Proceedings in Mathematics & Statistics 120, 43-53 (2015). MSC: 78A46 93C20 35Q60 78M10 65N15 65N30 78M50 PDFBibTeX XMLCite \textit{J. B. Malmberg}, Springer Proc. Math. Stat. 120, 43--53 (2015; Zbl 1319.78014) Full Text: DOI
Sun, Tong Numerical smoothness and error analysis on WENO for the nonlinear conservation laws. (English) Zbl 1286.65113 Numer. Methods Partial Differ. Equations 29, No. 6, 1881-1911 (2013). Reviewer: Vit Dolejsi (Praha) MSC: 65M15 65M08 65M06 35L65 PDFBibTeX XMLCite \textit{T. Sun}, Numer. Methods Partial Differ. Equations 29, No. 6, 1881--1911 (2013; Zbl 1286.65113) Full Text: DOI
Koshev, N.; Beilina, L. A posteriori error estimates for Fredholm integral equations of the first kind. (English) Zbl 1278.65198 Beilina, Larisa (ed.), Applied inverse problems. Select contributions from the first annual workshop on inverse problems, Gothenburg, Sweden, June 2–3, 2011. New York, NY: Springer (ISBN 978-1-4614-7815-7/hbk; 978-1-4614-7816-4/ebook). Springer Proceedings in Mathematics & Statistics 48, 75-93 (2013). MSC: 65R20 45A05 45B05 65R30 PDFBibTeX XMLCite \textit{N. Koshev} and \textit{L. Beilina}, Springer Proc. Math. Stat. 48, 75--93 (2013; Zbl 1278.65198) Full Text: DOI
Koshev, Nikolay; Beilina, Larisa An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data. (English) Zbl 1312.65225 Cent. Eur. J. Math. 11, No. 8, 1489-1509 (2013). Reviewer: Lehel Banjai (Edinburgh) MSC: 65R20 65R30 45B05 45A05 PDFBibTeX XMLCite \textit{N. Koshev} and \textit{L. Beilina}, Cent. Eur. J. Math. 11, No. 8, 1489--1509 (2013; Zbl 1312.65225) Full Text: DOI
Baccouch, Mahboub A local discontinuous Galerkin method for the second-order wave equation. (English) Zbl 1243.65119 Comput. Methods Appl. Mech. Eng. 209-212, 129-143 (2012). MSC: 65M60 PDFBibTeX XMLCite \textit{M. Baccouch}, Comput. Methods Appl. Mech. Eng. 209--212, 129--143 (2012; Zbl 1243.65119) Full Text: DOI
Asadzadeh, M.; Rostamy, D.; Zabihi, F. A posteriori error estimates for a coupled wave system with a local damping. (English. Russian original) Zbl 1283.65089 J. Math. Sci., New York 175, No. 3, 228-248 (2011); translation from Probl. Mat. Anal. 56, 17-34 (2011). MSC: 65M15 65M60 65M12 35L05 PDFBibTeX XMLCite \textit{M. Asadzadeh} et al., J. Math. Sci., New York 175, No. 3, 228--248 (2011; Zbl 1283.65089); translation from Probl. Mat. Anal. 56, 17--34 (2011) Full Text: DOI
Nazarov, Murtazo; Hoffman, Johan An adaptive finite element method for inviscid compressible flow. (English) Zbl 1427.76139 Int. J. Numer. Methods Fluids 64, No. 10-12, 1102-1128 (2010). MSC: 76M10 65M15 76N15 35Q31 PDFBibTeX XMLCite \textit{M. Nazarov} and \textit{J. Hoffman}, Int. J. Numer. Methods Fluids 64, No. 10--12, 1102--1128 (2010; Zbl 1427.76139) Full Text: DOI
Adjerid, Slimane; Baccouch, Mahboub Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem. (English) Zbl 1196.65152 Appl. Numer. Math. 60, No. 9, 903-914 (2010). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65M15 PDFBibTeX XMLCite \textit{S. Adjerid} and \textit{M. Baccouch}, Appl. Numer. Math. 60, No. 9, 903--914 (2010; Zbl 1196.65152) Full Text: DOI
Adjerid, Slimane; Weinhart, Thomas Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems. (English) Zbl 1229.65166 Comput. Methods Appl. Mech. Eng. 198, No. 37-40, 3113-3129 (2009). MSC: 65M15 65M60 PDFBibTeX XMLCite \textit{S. Adjerid} and \textit{T. Weinhart}, Comput. Methods Appl. Mech. Eng. 198, No. 37--40, 3113--3129 (2009; Zbl 1229.65166) Full Text: DOI
Adjerid, Slimane; Baccouch, Mahboub The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation. (English) Zbl 1203.65241 J. Sci. Comput. 38, No. 1, 15-49 (2009). MSC: 65N30 35A35 35L70 65N15 PDFBibTeX XMLCite \textit{S. Adjerid} and \textit{M. Baccouch}, J. Sci. Comput. 38, No. 1, 15--49 (2009; Zbl 1203.65241) Full Text: DOI
Izadi, Mohammad A posteriori error estimates for the coupling equations of scalar conservation laws. (English) Zbl 1190.65138 BIT 49, No. 4, 697-720 (2009). Reviewer: Iwan Gawriljuk (Eisenach) MSC: 65M15 65M60 35L65 PDFBibTeX XMLCite \textit{M. Izadi}, BIT 49, No. 4, 697--720 (2009; Zbl 1190.65138) Full Text: DOI
Ohlberger, Mario A review of a posteriori error control and adaptivity for approximations of non-linear conservation laws. (English) Zbl 1185.65163 Int. J. Numer. Methods Fluids 59, No. 3, 333-354 (2009). MSC: 65M15 PDFBibTeX XMLCite \textit{M. Ohlberger}, Int. J. Numer. Methods Fluids 59, No. 3, 333--354 (2009; Zbl 1185.65163) Full Text: DOI
Bourgault, Y.; Picasso, M.; Alauzet, F.; Loseille, A. On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows. (English) Zbl 1391.76462 Int. J. Numer. Methods Fluids 59, No. 1, 47-74 (2009). MSC: 76M20 65M06 65M15 76N15 PDFBibTeX XMLCite \textit{Y. Bourgault} et al., Int. J. Numer. Methods Fluids 59, No. 1, 47--74 (2009; Zbl 1391.76462) Full Text: DOI
Moon, K.-S.; von Schwerin, E.; Szepessy, A.; Tempone, R. Convergence rates for an adaptive dual weighted residual finite element algorithm. (English) Zbl 1101.65103 BIT 46, No. 2, 367-407 (2006). Reviewer: Dietrich Braess (Bochum) MSC: 65N12 65N50 65N30 65N15 PDFBibTeX XMLCite \textit{K. S. Moon} et al., BIT 46, No. 2, 367--407 (2006; Zbl 1101.65103) Full Text: DOI
Ferm, Lars; Lötstedt, Per Space-time adaptive solution of first order PDEs. (English) Zbl 1089.76041 J. Sci. Comput. 26, No. 1, 83-110 (2006). MSC: 76M20 76N15 65M12 65M50 PDFBibTeX XMLCite \textit{L. Ferm} and \textit{P. Lötstedt}, J. Sci. Comput. 26, No. 1, 83--110 (2006; Zbl 1089.76041) Full Text: DOI
Akrivis, Georgios; Makridakis, Charalambos; Nochetto, Ricardo H. A posteriori error estimates for the Crank-Nicolson method for parabolic equations. (English) Zbl 1101.65094 Math. Comput. 75, No. 254, 511-531 (2006). Reviewer: Jiří Vaníček (Praha) MSC: 65M15 65M50 65M60 35K55 35K15 65M06 PDFBibTeX XMLCite \textit{G. Akrivis} et al., Math. Comput. 75, No. 254, 511--531 (2006; Zbl 1101.65094) Full Text: DOI
Ohlberger, Mario; Vovelle, Julien Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method. (English) Zbl 1082.65112 Math. Comput. 75, No. 253, 113-150 (2006). Reviewer: Qin Mengzhao (Beijing) MSC: 65N15 65N30 35A35 35L65 PDFBibTeX XMLCite \textit{M. Ohlberger} and \textit{J. Vovelle}, Math. Comput. 75, No. 253, 113--150 (2006; Zbl 1082.65112) Full Text: DOI
Chen, Zhiming; Ji, Guanghua Sharp \(L^1\) a posteriori error analysis for nonlinear convection-diffusion problems. (English) Zbl 1107.65080 Math. Comput. 75, No. 253, 43-71 (2006). Reviewer: Jialin Hong (Beijing) MSC: 65M15 35K55 PDFBibTeX XMLCite \textit{Z. Chen} and \textit{G. Ji}, Math. Comput. 75, No. 253, 43--71 (2006; Zbl 1107.65080) Full Text: DOI
Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E. Convergence rates for adaptive weak approximation of stochastic differential equations. (English) Zbl 1079.65012 Stochastic Anal. Appl. 23, No. 3, 511-558 (2005). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 65Y20 65L50 60H35 60H10 PDFBibTeX XMLCite \textit{K.-S. Moon} et al., Stochastic Anal. Appl. 23, No. 3, 511--558 (2005; Zbl 1079.65012) Full Text: DOI
Klöfkorn, Robert; Kröner, Dietmar; Ohlberger, Mario Local adaptive methods for convection dominated problems. (English) Zbl 1058.76576 Int. J. Numer. Methods Fluids 40, No. 1-2, 79-91 (2002). MSC: 76M12 76R99 76Z99 PDFBibTeX XMLCite \textit{R. Klöfkorn} et al., Int. J. Numer. Methods Fluids 40, No. 1--2, 79--91 (2002; Zbl 1058.76576) Full Text: DOI
Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E. Adaptive weak approximation of stochastic differential equations. (English) Zbl 1024.60028 Commun. Pure Appl. Math. 54, No. 10, 1169-1214 (2001). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H35 60H10 65C30 65C05 PDFBibTeX XMLCite \textit{A. Szepessy} et al., Commun. Pure Appl. Math. 54, No. 10, 1169--1214 (2001; Zbl 1024.60028) Full Text: DOI
Mackerle, Jaroslav Error estimates and adaptive finite element methods. A bibliography (1990–2000). (English) Zbl 0985.65140 Eng. Comput. (Bradf.) 18, No. 5-6, 802-914 (2001). MSC: 65N30 74S05 65N15 65-00 74-00 65M60 65M15 78M10 PDFBibTeX XMLCite \textit{J. Mackerle}, Eng. Comput. (Bradf.) 18, No. 5--6, 802--914 (2001; Zbl 0985.65140) Full Text: DOI
Thomas, Ingo; Sonar, Thomas On a second order residual estimator for numerical schemes for nonlinear hyperbolic conservation laws. (English) Zbl 0985.65109 J. Comput. Phys. 171, No. 1, 227-242 (2001). MSC: 65M15 65M06 35L65 65M50 PDFBibTeX XMLCite \textit{I. Thomas} and \textit{T. Sonar}, J. Comput. Phys. 171, No. 1, 227--242 (2001; Zbl 0985.65109) Full Text: DOI
Arvanitis, Christos; Katsaounis, Theodoros; Makridakis, Charalambos Adaptive finite element relaxation schemes for hyperbolic conservation laws. (English) Zbl 0980.65104 M2AN, Math. Model. Numer. Anal. 35, No. 1, 17-33 (2001). Reviewer: Mária Lukáčová (Brno) MSC: 65M60 35L65 65M50 35Q53 74S05 65M20 65M12 74B20 PDFBibTeX XMLCite \textit{C. Arvanitis} et al., M2AN, Math. Model. Numer. Anal. 35, No. 1, 17--33 (2001; Zbl 0980.65104) Full Text: DOI Numdam EuDML
Burman, E. Adaptive finite element methods for compressible two-phase flow. (English) Zbl 1018.76024 Math. Models Methods Appl. Sci. 10, No. 7, 963-989 (2000). MSC: 76M10 76T10 65M50 PDFBibTeX XMLCite \textit{E. Burman}, Math. Models Methods Appl. Sci. 10, No. 7, 963--989 (2000; Zbl 1018.76024) Full Text: DOI
Asadzadeh, Mohammad A posteriori error estimates for the Fokker-Planck and Fermi pencil beam equations. (English) Zbl 1012.82008 Math. Models Methods Appl. Sci. 10, No. 5, 737-769 (2000). MSC: 82B80 65M60 35Q40 PDFBibTeX XMLCite \textit{M. Asadzadeh}, Math. Models Methods Appl. Sci. 10, No. 5, 737--769 (2000; Zbl 1012.82008) Full Text: DOI
Burman, Erik Adaptive finite element methods for compressible flow. (English) Zbl 0973.76040 Comput. Methods Appl. Mech. Eng. 190, No. 8-10, 1137-1162 (2000). MSC: 76M10 76N15 65M15 PDFBibTeX XMLCite \textit{E. Burman}, Comput. Methods Appl. Mech. Eng. 190, No. 8--10, 1137--1162 (2000; Zbl 0973.76040) Full Text: DOI
Perotto, S.; Saleri, F. Adaptive finite element methods for Boussinesq equations. (English) Zbl 0951.65099 Numer. Methods Partial Differ. Equations 16, No. 2, 214-236 (2000). Reviewer: V.P.Tyagi (Bombay) MSC: 65M60 65M15 35Q53 PDFBibTeX XMLCite \textit{S. Perotto} and \textit{F. Saleri}, Numer. Methods Partial Differ. Equations 16, No. 2, 214--236 (2000; Zbl 0951.65099) Full Text: DOI
Wang, Hong; Ewing, Richard E.; Qin, Guan; Lyons, Stephen L.; Al-Lawatia, Mohamed; Man, Shushuang A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations. (English) Zbl 0956.76050 J. Comput. Phys. 152, No. 1, 120-163 (1999). MSC: 76M10 76R99 PDFBibTeX XMLCite \textit{H. Wang} et al., J. Comput. Phys. 152, No. 1, 120--163 (1999; Zbl 0956.76050) Full Text: DOI
Andrews, J. G.; Morton, K. W. A posteriori error estimation based on discrepancies in an entropy variable. (English) Zbl 0933.76049 Int. J. Comput. Fluid Dyn. 10, No. 3, 183-198 (1998). MSC: 76M12 76N15 PDFBibTeX XMLCite \textit{J. G. Andrews} and \textit{K. W. Morton}, Int. J. Comput. Fluid Dyn. 10, No. 3, 183--198 (1998; Zbl 0933.76049) Full Text: DOI
Repin, S. I. A posteriori error estimation for nonlinear variational problems by duality theory. (English) Zbl 0904.65064 J. Math. Sci., New York 99, No. 1, 927-935 (2000); translation from Zap. Nauchn. Semin. POMI 243, 201-214 (1997). MSC: 65K10 49J27 49N15 PDFBibTeX XMLCite \textit{S. I. Repin}, J. Math. Sci., New York 99, No. 1, 927--935 (1997; Zbl 0904.65064); translation from Zap. Nauchn. Semin. POMI 243, 201--214 (1997) Full Text: DOI