Mallik, Gouranga; Gudi, Thirupathi A hybrid high-order method for a class of strongly nonlinear elliptic boundary value problems. (English) Zbl 07784040 J. Sci. Comput. 98, No. 1, Paper No. 6, 26 p. (2024). MSC: 65N30 65N12 65N15 35J66 35J57 47H10 35A01 35A02 PDFBibTeX XMLCite \textit{G. Mallik} and \textit{T. Gudi}, J. Sci. Comput. 98, No. 1, Paper No. 6, 26 p. (2024; Zbl 07784040) Full Text: DOI arXiv
Pitassi, Silvano; Ghiloni, Riccardo; Petretti, Igor; Trevisan, Francesco; Specogna, Ruben The curved mimetic finite difference method: allowing grids with curved faces. (English) Zbl 07715227 J. Comput. Phys. 490, Article ID 112294, 18 p. (2023). MSC: 65Nxx 35Jxx 76Mxx PDFBibTeX XMLCite \textit{S. Pitassi} et al., J. Comput. Phys. 490, Article ID 112294, 18 p. (2023; Zbl 07715227) Full Text: DOI arXiv
Artioli, Edoardo; de Miranda, Stefano; Lovadina, Carlo; Patruno, Luca; Visinoni, Michele Some virtual element methods for infinitesimal elasticity problems. (English) Zbl 1503.65285 Antonietti, Paola F. (ed.) et al., The virtual element method and its applications. Cham: Birkhäuser. SEMA SIMAI Springer Ser. 31, 137-183 (2022). MSC: 65N30 65N12 35A15 74B10 74S05 35Q74 PDFBibTeX XMLCite \textit{E. Artioli} et al., SEMA SIMAI Springer Ser. 31, 137--183 (2022; Zbl 1503.65285) Full Text: DOI
Li, Yang; Hu, Chaolang; Feng, Minfu A least-squares stabilization virtual element method for the Stokes problem on polygonal meshes. (English) Zbl 1513.65467 Int. J. Numer. Anal. Model. 19, No. 5, 685-708 (2022). MSC: 65N30 65N12 76D07 76M10 65N15 PDFBibTeX XMLCite \textit{Y. Li} et al., Int. J. Numer. Anal. Model. 19, No. 5, 685--708 (2022; Zbl 1513.65467) Full Text: Link
Gudi, Thirupathi; Mallik, Gouranga; Pramanick, Tamal A hybrid high-order method for quasilinear elliptic problems of nonmonotone type. (English) Zbl 1501.65119 SIAM J. Numer. Anal. 60, No. 4, 2318-2344 (2022). Reviewer: Vit Dolejsi (Praha) MSC: 65N30 65N12 65N15 35J62 37C25 PDFBibTeX XMLCite \textit{T. Gudi} et al., SIAM J. Numer. Anal. 60, No. 4, 2318--2344 (2022; Zbl 1501.65119) Full Text: DOI arXiv
Manzini, Gianmarco; Mazzia, Annamaria Conforming virtual element approximations of the two-dimensional Stokes problem. (English) Zbl 1502.65212 Appl. Numer. Math. 181, 176-203 (2022). MSC: 65N30 65N12 65N15 76D07 76M10 35Q35 PDFBibTeX XMLCite \textit{G. Manzini} and \textit{A. Mazzia}, Appl. Numer. Math. 181, 176--203 (2022; Zbl 1502.65212) Full Text: DOI arXiv
Manzini, Gianmarco; Mazzia, Annamaria A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem. (English) Zbl 1492.65324 J. Comput. Dyn. 9, No. 2, 207-238 (2022). Reviewer: Francesca Gardini (Pavia) MSC: 65N30 65N22 65N12 65N15 76D07 76M10 35B45 35Q35 PDFBibTeX XMLCite \textit{G. Manzini} and \textit{A. Mazzia}, J. Comput. Dyn. 9, No. 2, 207--238 (2022; Zbl 1492.65324) Full Text: DOI arXiv
Jahandari, Hormoz; Bihlo, Alex Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method. (English) Zbl 1460.86003 Comput. Geosci. 25, No. 3, 1083-1104 (2021). MSC: 86-08 86A25 65N06 PDFBibTeX XMLCite \textit{H. Jahandari} and \textit{A. Bihlo}, Comput. Geosci. 25, No. 3, 1083--1104 (2021; Zbl 1460.86003) Full Text: DOI
Sreekumar, Abhilash; Triantafyllou, Savvas P.; Bécot, François-Xavier; Chevillotte, Fabien Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains. (English) Zbl 1506.74445 Comput. Methods Appl. Mech. Eng. 375, Article ID 113543, 44 p. (2021). MSC: 74S05 65N30 74F10 74M25 PDFBibTeX XMLCite \textit{A. Sreekumar} et al., Comput. Methods Appl. Mech. Eng. 375, Article ID 113543, 44 p. (2021; Zbl 1506.74445) Full Text: DOI
Pitassi, Silvano; Trevisan, Francesco; Specogna, Ruben Explicit geometric construction of sparse inverse mass matrices for arbitrary tetrahedral grids. (English) Zbl 1506.65143 Comput. Methods Appl. Mech. Eng. 377, Article ID 113699, 20 p. (2021). MSC: 65M22 PDFBibTeX XMLCite \textit{S. Pitassi} et al., Comput. Methods Appl. Mech. Eng. 377, Article ID 113699, 20 p. (2021; Zbl 1506.65143) Full Text: DOI arXiv
Dong, Qiannan; Wu, Jiming; Su, Shuai Relationship between the vertex-centered linearity-preserving scheme and the lowest-order virtual element method for diffusion problems on star-shaped polygons. (English) Zbl 1446.65164 Comput. Math. Appl. 79, No. 11, 3117-3138 (2020). MSC: 65N30 65N08 35J25 PDFBibTeX XMLCite \textit{Q. Dong} et al., Comput. Math. Appl. 79, No. 11, 3117--3138 (2020; Zbl 1446.65164) Full Text: DOI
Ooi, E. T.; Saputra, A.; Natarajan, S.; Ooi, E. H.; Song, C. A dual scaled boundary finite element formulation over arbitrary faceted star convex polyhedra. (English) Zbl 1464.74195 Comput. Mech. 66, No. 1, 27-47 (2020). MSC: 74S05 74K99 PDFBibTeX XMLCite \textit{E. T. Ooi} et al., Comput. Mech. 66, No. 1, 27--47 (2020; Zbl 1464.74195) Full Text: DOI
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
Liu, Xin; Li, Rui; Chen, Zhangxin A virtual element method for the coupled Stokes-Darcy problem with the Beaver-Joseph-Saffman interface condition. (English) Zbl 1471.65200 Calcolo 56, No. 4, Paper No. 48, 28 p. (2019). Reviewer: Lijun Yi (Shanghai) MSC: 65N30 65N12 65N15 76D07 76S05 76M10 PDFBibTeX XMLCite \textit{X. Liu} et al., Calcolo 56, No. 4, Paper No. 48, 28 p. (2019; Zbl 1471.65200) Full Text: DOI
Manzini, Gianmarco; Maguolo, Gianluca; Putti, Mario The high-order mixed mimetic finite difference method for time-dependent diffusion problems. (English) Zbl 1428.65013 J. Sci. Comput. 80, No. 3, 1805-1830 (2019); correction ibid. 80, No. 3, 1831 (2019). MSC: 65M06 65M12 65M20 76R50 PDFBibTeX XMLCite \textit{G. Manzini} et al., J. Sci. Comput. 80, No. 3, 1805--1830 (2019; Zbl 1428.65013) Full Text: DOI
Repin, Sergey Poincaré type inequalities for vector functions with zero mean normal traces on the boundary and applications to interpolation methods. (English) Zbl 1416.35016 Chetverushkin, B. N. (ed.) et al., Contributions to partial differential equations and applications. Invited papers of the conferences ‘Contributions to partial differential equations’, Université Pierre et Marie Curie, Paris, France, August 31 – September 1, 2015 and ‘Applied and computational mathematics’, University of Houston, Texas, USA, February 26–27, 2016. Cham: Springer. Comput. Methods Appl. Sci. 47, 411-432 (2019). MSC: 35A23 PDFBibTeX XMLCite \textit{S. Repin}, Comput. Methods Appl. Sci. 47, 411--432 (2019; Zbl 1416.35016) Full Text: DOI arXiv Link
Liu, Xin; Chen, Zhangxin The nonconforming virtual element method for the Navier-Stokes equations. (English) Zbl 1419.65117 Adv. Comput. Math. 45, No. 1, 51-74 (2019). MSC: 65N30 65N12 65N15 76D05 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Z. Chen}, Adv. Comput. Math. 45, No. 1, 51--74 (2019; Zbl 1419.65117) Full Text: DOI
Scotti, Anna; Sottocasa, Federica Analysis of a mimetic finite difference approximation of flows in fractured porous media. (English) Zbl 1404.65228 ESAIM, Math. Model. Numer. Anal. 52, No. 2, 595-630 (2018). MSC: 65N12 65N99 76S05 28A80 65N06 05C82 PDFBibTeX XMLCite \textit{A. Scotti} and \textit{F. Sottocasa}, ESAIM, Math. Model. Numer. Anal. 52, No. 2, 595--630 (2018; Zbl 1404.65228) Full Text: DOI
Artioli, E.; de Miranda, S.; Lovadina, C.; Patruno, L. A stress/displacement virtual element method for plane elasticity problems. (English) Zbl 1439.74040 Comput. Methods Appl. Mech. Eng. 325, 155-174 (2017). MSC: 74B05 74S05 65N30 PDFBibTeX XMLCite \textit{E. Artioli} et al., Comput. Methods Appl. Mech. Eng. 325, 155--174 (2017; Zbl 1439.74040) Full Text: DOI arXiv
Liu, Xin; Li, Jian; Chen, Zhangxin A nonconforming virtual element method for the Stokes problem on general meshes. (English) Zbl 1439.76085 Comput. Methods Appl. Mech. Eng. 320, 694-711 (2017). MSC: 76M10 65N30 65N12 65N15 76D07 PDFBibTeX XMLCite \textit{X. Liu} et al., Comput. Methods Appl. Mech. Eng. 320, 694--711 (2017; Zbl 1439.76085) Full Text: DOI
Zou, Degao; Chen, Kai; Kong, Xianjing; Liu, Jingmao An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis. (English) Zbl 1403.74273 Eng. Anal. Bound. Elem. 84, 87-107 (2017). MSC: 74S15 74S05 65N38 PDFBibTeX XMLCite \textit{D. Zou} et al., Eng. Anal. Bound. Elem. 84, 87--107 (2017; Zbl 1403.74273) Full Text: DOI
Beirão da Veiga, Lourenco; Lopez, Luciano; Vacca, Giuseppe Mimetic finite difference methods for Hamiltonian wave equations in 2D. (English) Zbl 1448.65092 Comput. Math. Appl. 74, No. 5, 1123-1141 (2017). MSC: 65M06 65M12 35L20 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Comput. Math. Appl. 74, No. 5, 1123--1141 (2017; Zbl 1448.65092) Full Text: DOI arXiv
Meierbachtol, Collin S.; Svyatskiy, Daniil; Delzanno, Gian Luca; Vernon, Louis J.; Moulton, J. David An electrostatic particle-in-cell code on multi-block structured meshes. (English) Zbl 1380.65312 J. Comput. Phys. 350, 796-823 (2017). MSC: 65M75 82D10 65M50 PDFBibTeX XMLCite \textit{C. S. Meierbachtol} et al., J. Comput. Phys. 350, 796--823 (2017; Zbl 1380.65312) Full Text: DOI Link
Antonietti, Paola F.; Formaggia, Luca; Scotti, Anna; Verani, Marco; Verzott, Nicola Mimetic finite difference approximation of flows in fractured porous media. (English) Zbl 1381.76231 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 809-832 (2016). MSC: 76M20 65N06 76S05 65N30 35Q86 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 3, 809--832 (2016; Zbl 1381.76231) Full Text: DOI
Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro Mixed virtual element methods for general second order elliptic problems on polygonal meshes. (English) Zbl 1343.65134 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 727-747 (2016). Reviewer: H. P. Dikshit (Bhopal) MSC: 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 3, 727--747 (2016; Zbl 1343.65134) Full Text: DOI arXiv
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.; Brezzi, F.; Marini, L. D.; Russo, A. \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods. (English) Zbl 1343.65133 Numer. Math. 133, No. 2, 303-332 (2016). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Numer. Math. 133, No. 2, 303--332 (2016; Zbl 1343.65133) Full Text: DOI arXiv
Lopez, Luciano; Vacca, Giuseppe Spectral properties and conservation laws in mimetic finite difference methods for PDEs. (English) Zbl 1329.65250 J. Comput. Appl. Math. 292, 760-784 (2016). MSC: 65N06 65M06 35L65 35Q35 PDFBibTeX XMLCite \textit{L. Lopez} and \textit{G. Vacca}, J. Comput. Appl. Math. 292, 760--784 (2016; Zbl 1329.65250) Full Text: DOI
Antonietti, Paola F.; Verani, Marco; Zikatanov, Ludmil A two-level method for mimetic finite difference discretizations of elliptic problems. (English) Zbl 1443.65279 Comput. Math. Appl. 70, No. 11, 2674-2687 (2015). MSC: 65N06 65N55 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Comput. Math. Appl. 70, No. 11, 2674--2687 (2015; Zbl 1443.65279) Full Text: DOI arXiv
Gain, Arun L.; Paulino, Glaucio H.; Duarte, Leonardo S.; Menezes, Ivan F. M. Topology optimization using polytopes. (English) Zbl 1423.74745 Comput. Methods Appl. Mech. Eng. 293, 411-430 (2015). MSC: 74P15 74S05 65N30 PDFBibTeX XMLCite \textit{A. L. Gain} et al., Comput. Methods Appl. Mech. Eng. 293, 411--430 (2015; Zbl 1423.74745) Full Text: DOI arXiv
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
Dieter-Kissling, Kathrin; Marschall, Holger; Bothe, Dieter Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology. (English) Zbl 1390.76052 Comput. Fluids 109, 168-184 (2015). MSC: 76D05 76M25 PDFBibTeX XMLCite \textit{K. Dieter-Kissling} et al., Comput. Fluids 109, 168--184 (2015; Zbl 1390.76052) Full Text: DOI
Lemoine, A.; Caltagirone, J.-P.; Azaïez, M.; Vincent, S. Discrete Helmholtz-Hodge decomposition on polyhedral meshes using compatible discrete operators. (English) Zbl 1329.65249 J. Sci. Comput. 65, No. 1, 34-53 (2015). MSC: 65N06 65N12 35J25 65N50 PDFBibTeX XMLCite \textit{A. Lemoine} et al., J. Sci. Comput. 65, No. 1, 34--53 (2015; Zbl 1329.65249) Full Text: DOI
Yin, Li; Wu, Jiming; Gao, Zhiming The cell functional minimization scheme for the anisotropic diffusion problems on arbitrary polygonal grids. (English) Zbl 1314.65140 ESAIM, Math. Model. Numer. Anal. 49, No. 1, 193-220 (2015). Reviewer: Gisbert Stoyan (Budapest) MSC: 65N08 65N12 35J25 65N15 PDFBibTeX XMLCite \textit{L. Yin} et al., ESAIM, Math. Model. Numer. Anal. 49, No. 1, 193--220 (2015; Zbl 1314.65140) Full Text: DOI Link
Di Pietro, Daniele A.; Lemaire, Simon An extension of the Crouzeix-Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow. (English) Zbl 1308.74145 Math. Comput. 84, No. 291, 1-31 (2015). MSC: 74S05 76M10 74B05 76D07 65N30 65N08 PDFBibTeX XMLCite \textit{D. A. Di Pietro} and \textit{S. Lemaire}, Math. Comput. 84, No. 291, 1--31 (2015; Zbl 1308.74145) Full Text: DOI
Gain, Arun L.; Talischi, Cameron; Paulino, Glaucio H. On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes. (English) Zbl 1423.74095 Comput. Methods Appl. Mech. Eng. 282, 132-160 (2014). MSC: 74B05 65N30 74S05 PDFBibTeX XMLCite \textit{A. L. Gain} et al., Comput. Methods Appl. Mech. Eng. 282, 132--160 (2014; Zbl 1423.74095) Full Text: DOI arXiv
Bishop, J. E. A displacement-based finite element formulation for general polyhedra using harmonic shape functions. (English) Zbl 1352.74326 Int. J. Numer. Methods Eng. 97, No. 1, 1-31 (2014). MSC: 74S05 65N30 PDFBibTeX XMLCite \textit{J. E. Bishop}, Int. J. Numer. Methods Eng. 97, No. 1, 1--31 (2014; Zbl 1352.74326) Full Text: DOI Link
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail Mimetic finite difference method. (English) Zbl 1352.65420 J. Comput. Phys. 257, Part B, 1163-1227 (2014). MSC: 65N06 65M06 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 257, Part B, 1163--1227 (2014; Zbl 1352.65420) Full Text: DOI
Yin, Li; Wu, Jiming; Yao, Yanzhong A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes. (English) Zbl 1307.65128 Numer. Math. 128, No. 4, 773-804 (2014). Reviewer: H. P. Dikshit (Bhopal) MSC: 65M55 65M12 65M60 65M15 35K55 PDFBibTeX XMLCite \textit{L. Yin} et al., Numer. Math. 128, No. 4, 773--804 (2014; Zbl 1307.65128) Full Text: DOI
Manzini, Gianmarco; Russo, Alessandro; Sukumar, N. New perspectives on polygonal and polyhedral finite element methods. (English) Zbl 1291.65322 Math. Models Methods Appl. Sci. 24, No. 8, 1665-1699 (2014). MSC: 65N06 65N12 65F05 PDFBibTeX XMLCite \textit{G. Manzini} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1665--1699 (2014; Zbl 1291.65322) Full Text: DOI
Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco; Svyatskiy, Daniil M-adaptation in the mimetic finite difference method. (English) Zbl 1291.65320 Math. Models Methods Appl. Sci. 24, No. 8, 1621-1663 (2014). MSC: 65N06 65N12 65F05 PDFBibTeX XMLCite \textit{V. Gyrya} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1621--1663 (2014; Zbl 1291.65320) Full Text: DOI
Droniou, Jerome Finite volume schemes for diffusion equations: introduction to and review of modern methods. (English) Zbl 1291.65319 Math. Models Methods Appl. Sci. 24, No. 8, 1575-1619 (2014). MSC: 65N06 65N08 65N12 65N15 65N30 PDFBibTeX XMLCite \textit{J. Droniou}, Math. Models Methods Appl. Sci. 24, No. 8, 1575--1619 (2014; Zbl 1291.65319) Full Text: DOI arXiv
Beirão da Veiga, L.; Brezzi, Franco; Marini, L. D.; Russo, A. The Hitchhiker’s guide to the virtual element method. (English) Zbl 1291.65336 Math. Models Methods Appl. Sci. 24, No. 8, 1541-1573 (2014). MSC: 65N30 65N12 65-01 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1541--1573 (2014; Zbl 1291.65336) Full Text: DOI
Antonietti, P. F.; Beirão da Veiga, L.; Bigoni, N.; Verani, M. Mimetic finite differences for nonlinear and control problems. (English) Zbl 1291.65316 Math. Models Methods Appl. Sci. 24, No. 8, 1457-1493 (2014). MSC: 65N06 65N20 35J62 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1457--1493 (2014; Zbl 1291.65316) Full Text: DOI
Lipnikov, Konstantin; Reynolds, James; Nelson, Eric Mimetic discretization of two-dimensional magnetic diffusion equations. (English) Zbl 1349.78095 J. Comput. Phys. 247, 1-16 (2013). MSC: 78M20 65M06 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 247, 1--16 (2013; Zbl 1349.78095) Full Text: DOI
Ahmad, B.; Alsaedi, A.; Brezzi, F.; Marini, L. D.; Russo, A. Equivalent projectors for virtual element methods. (English) Zbl 1347.65172 Comput. Math. Appl. 66, No. 3, 376-391 (2013). MSC: 65N30 65N06 PDFBibTeX XMLCite \textit{B. Ahmad} et al., Comput. Math. Appl. 66, No. 3, 376--391 (2013; Zbl 1347.65172) Full Text: DOI
Brezzi, Franco; Marini, L. Donatella Virtual element methods for plate bending problems. (English) Zbl 1297.74049 Comput. Methods Appl. Mech. Eng. 253, 455-462 (2013). MSC: 74G60 74S05 65N30 74K20 PDFBibTeX XMLCite \textit{F. Brezzi} and \textit{L. D. Marini}, Comput. Methods Appl. Mech. Eng. 253, 455--462 (2013; Zbl 1297.74049) Full Text: DOI
Sun, Weiwei; Wu, Jiming; Zhang, Xiaoping A family of linearity-preserving schemes for anisotropic diffusion problems on arbitrary polyhedral grids. (English) Zbl 1286.76138 Comput. Methods Appl. Mech. Eng. 267, 418-433 (2013). MSC: 76R50 76M12 65N08 PDFBibTeX XMLCite \textit{W. Sun} et al., Comput. Methods Appl. Mech. Eng. 267, 418--433 (2013; Zbl 1286.76138) Full Text: DOI
Beirão da Veiga, Lourenço; Lovadina, Carlo; Mora, David Numerical results for mimetic discretization of Reissner-Mindlin plate problems. (English) Zbl 1273.65172 Calcolo 50, No. 3, 209-237 (2013). MSC: 65N30 74K20 65N25 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Calcolo 50, No. 3, 209--237 (2013; Zbl 1273.65172) Full Text: DOI arXiv
Antonietti, Paola F.; Beirão da Veiga, Lourenço; Verani, Marco A mimetic discretization of elliptic obstacle problems. (English) Zbl 1271.65136 Math. Comput. 82, No. 283, 1379-1400 (2013). MSC: 65N30 35J25 35R35 65N12 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Math. Comput. 82, No. 283, 1379--1400 (2013; Zbl 1271.65136) Full Text: DOI
Beirão da Veiga, L.; Brezzi, F.; Cangiani, A.; Manzini, G.; Marini, L. D.; Russo, A. Basic principles of virtual element methods. (English) Zbl 1416.65433 Math. Models Methods Appl. Sci. 23, No. 1, 199-214 (2013). Reviewer: Qin Meng Zhao (Beijing) MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Math. Models Methods Appl. Sci. 23, No. 1, 199--214 (2013; Zbl 1416.65433) Full Text: DOI
Lashuk, I. V.; Vassilevski, P. S. Element agglomeration coarse Raviart-Thomas spaces with improved approximation properties. (English) Zbl 1274.65302 Numer. Linear Algebra Appl. 19, No. 2, 414-426 (2012). MSC: 65N30 65N55 35J25 PDFBibTeX XMLCite \textit{I. V. Lashuk} and \textit{P. S. Vassilevski}, Numer. Linear Algebra Appl. 19, No. 2, 414--426 (2012; Zbl 1274.65302) Full Text: DOI
Jiang, Lijian; Moulton, J. David; Svyatskiy, Daniil Analysis of stochastic mimetic finite difference methods and their applications in single-phase stochastic flows. (English) Zbl 1253.76121 Comput. Methods Appl. Mech. Eng. 217-220, 58-76 (2012). MSC: 76R50 76M35 76M20 60G35 60H35 PDFBibTeX XMLCite \textit{L. Jiang} et al., Comput. Methods Appl. Mech. Eng. 217--220, 58--76 (2012; Zbl 1253.76121) Full Text: DOI
Karasözen, Bülent; Trofimova, Anastasia V.; Tsybulin, Vyacheslav G. Natural convection in porous annular domains: Mimetic scheme and family of steady states. (English) Zbl 1386.76113 J. Comput. Phys. 231, No. 7, 2995-3005 (2012). MSC: 76M20 76R10 76S05 76E05 PDFBibTeX XMLCite \textit{B. Karasözen} et al., J. Comput. Phys. 231, No. 7, 2995--3005 (2012; Zbl 1386.76113) Full Text: DOI
Sheng, Zhiqiang; Yuan, Guangwei An improved monotone finite volume scheme for diffusion equation on polygonal meshes. (English) Zbl 1242.65219 J. Comput. Phys. 231, No. 9, 3739-3754 (2012). MSC: 65N08 35J25 65N50 PDFBibTeX XMLCite \textit{Z. Sheng} and \textit{G. Yuan}, J. Comput. Phys. 231, No. 9, 3739--3754 (2012; Zbl 1242.65219) Full Text: DOI
Gyrya, V.; Lipnikov, K.; Aranson, I. S.; Berlyand, L. Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations. (English) Zbl 1232.92032 J. Math. Biol. 62, No. 5, 707-740 (2011). MSC: 92C17 35Q92 92C05 92C35 92-08 PDFBibTeX XMLCite \textit{V. Gyrya} et al., J. Math. Biol. 62, No. 5, 707--740 (2011; Zbl 1232.92032) Full Text: DOI
Cangiani, Andrea; Gardini, Francesca; Manzini, Gianmarco Convergence of the mimetic finite difference method for eigenvalue problems in mixed form. (English) Zbl 1225.65106 Comput. Methods Appl. Mech. Eng. 200, No. 9-12, 1150-1160 (2011). MSC: 65N25 65N12 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Comput. Methods Appl. Mech. Eng. 200, No. 9--12, 1150--1160 (2011; Zbl 1225.65106) Full Text: DOI
Sheng, Zhiqiang; Yuan, Guangwei The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes. (English) Zbl 1218.65120 J. Comput. Phys. 230, No. 7, 2588-2604 (2011). MSC: 65N08 35J25 65N50 PDFBibTeX XMLCite \textit{Z. Sheng} and \textit{G. Yuan}, J. Comput. Phys. 230, No. 7, 2588--2604 (2011; Zbl 1218.65120) Full Text: DOI
Garimella, R. V.; Lipnikov, K. Solution of the diffusion equation in multi-material domains by sub-division of elements along reconstructed interfaces. (English) Zbl 1429.76100 Int. J. Numer. Methods Fluids 65, No. 11-12, 1423-1437 (2011). MSC: 76R50 76T30 65M50 PDFBibTeX XMLCite \textit{R. V. Garimella} and \textit{K. Lipnikov}, Int. J. Numer. Methods Fluids 65, No. 11--12, 1423--1437 (2011; Zbl 1429.76100) Full Text: DOI
Beirão da Veiga, L.; Mora, D. A mimetic discretization of the Reissner-Mindlin plate bending problem. (English) Zbl 1428.74132 Numer. Math. 117, No. 3, 425-462 (2011). MSC: 74K20 74S20 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} and \textit{D. Mora}, Numer. Math. 117, No. 3, 425--462 (2011; Zbl 1428.74132) Full Text: DOI
Lipnikov, K.; Manzini, G.; Brezzi, F.; Buffa, A. The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes. (English) Zbl 1207.78041 J. Comput. Phys. 230, No. 2, 305-328 (2011). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M20 78A30 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 230, No. 2, 305--328 (2011; Zbl 1207.78041) Full Text: DOI
Yin, Li; Wu, Jiming; Yao, Yanzhong A cell functional minimization scheme for parabolic problem. (English) Zbl 1206.65217 J. Comput. Phys. 229, No. 23, 8935-8951 (2010). Reviewer: Petr Sváček (Praha) MSC: 65M08 35K20 35K55 65M55 65Y05 PDFBibTeX XMLCite \textit{L. Yin} et al., J. Comput. Phys. 229, No. 23, 8935--8951 (2010; Zbl 1206.65217) Full Text: DOI
Lipnikov, K.; Shashkov, M. A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes. (English) Zbl 1425.76186 J. Comput. Phys. 229, No. 20, 7911-7941 (2010). MSC: 76M25 PDFBibTeX XMLCite \textit{K. Lipnikov} and \textit{M. Shashkov}, J. Comput. Phys. 229, No. 20, 7911--7941 (2010; Zbl 1425.76186) Full Text: DOI
Brezzi, Franco; Buffa, Annalisa Innovative mimetic discretizations for electromagnetic problems. (English) Zbl 1191.78056 J. Comput. Appl. Math. 234, No. 6, 1980-1987 (2010). MSC: 78M20 65N30 78A25 PDFBibTeX XMLCite \textit{F. Brezzi} and \textit{A. Buffa}, J. Comput. Appl. Math. 234, No. 6, 1980--1987 (2010; Zbl 1191.78056) Full Text: DOI
Beirão da Veiga, Lourenco A mimetic discretization method for linear elasticity. (English) Zbl 1258.74206 ESAIM, Math. Model. Numer. Anal. 44, No. 2, 231-250 (2010). MSC: 74S20 74S05 65N06 74B05 65N30 PDFBibTeX XMLCite \textit{L. Beirão da Veiga}, ESAIM, Math. Model. Numer. Anal. 44, No. 2, 231--250 (2010; Zbl 1258.74206) Full Text: DOI EuDML
Droniou, Jérôme; Eymard, Robert; Gallouët, Thierry; Herbin, Raphaèle A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods. (English) Zbl 1191.65142 Math. Models Methods Appl. Sci. 20, No. 2, 265-295 (2010). Reviewer: Angela Handlovičová (Bratislava) MSC: 65N08 65N12 65N06 35J25 65N15 PDFBibTeX XMLCite \textit{J. Droniou} et al., Math. Models Methods Appl. Sci. 20, No. 2, 265--295 (2010; Zbl 1191.65142) Full Text: DOI arXiv
Beirão da Veiga, L.; Gyrya, V.; Lipnikov, K.; Manzini, G. Mimetic finite difference method for the Stokes problem on polygonal meshes. (English) Zbl 1172.76032 J. Comput. Phys. 228, No. 19, 7215-7232 (2009). MSC: 76M20 76D07 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., J. Comput. Phys. 228, No. 19, 7215--7232 (2009; Zbl 1172.76032) Full Text: DOI Link
Beirão da Veiga, L.; Lipnikov, K.; Manzini, G. Convergence analysis of the high-order mimetic finite difference method. (English) Zbl 1183.65132 Numer. Math. 113, No. 3, 325-356 (2009). Reviewer: Vit Dolejsi (Praha) MSC: 65N12 65N06 35J25 65N15 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Numer. Math. 113, No. 3, 325--356 (2009; Zbl 1183.65132) Full Text: DOI
Hermeline, F. A finite volume method for approximating 3D diffusion operators on general meshes. (English) Zbl 1168.76340 J. Comput. Phys. 228, No. 16, 5763-5786 (2009). MSC: 76M15 65N30 76A05 PDFBibTeX XMLCite \textit{F. Hermeline}, J. Comput. Phys. 228, No. 16, 5763--5786 (2009; Zbl 1168.76340) Full Text: DOI
Brezzi, Franco; Buffa, Annalisa; Lipnikov, Konstantin Mimetic finite differences for elliptic problems. (English) Zbl 1177.65164 ESAIM, Math. Model. Numer. Anal. 43, No. 2, 277-295 (2009). Reviewer: Georg Hebermehl (Berlin) MSC: 65N06 65N12 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{F. Brezzi} et al., ESAIM, Math. Model. Numer. Anal. 43, No. 2, 277--295 (2009; Zbl 1177.65164) Full Text: DOI EuDML Link
Aarnes, Jørg E.; Lie, Knut-Andreas; Kippe, Vegard; Krogstad, Stein Multiscale methods for subsurface flow. (English) Zbl 1364.76151 Engquist, Björn (ed.) et al., Multiscale modeling and simulation in science. Papers based on the presentations at the summer school, Bosön, Stockholm, Sweden, June 2007. Berlin: Springer (ISBN 978-3-540-88856-7/pbk; 978-3-540-88857-4/ebook). Lecture Notes in Computational Science and Engineering 66, 3-48 (2009). MSC: 76M25 76B15 86A05 PDFBibTeX XMLCite \textit{J. E. Aarnes} et al., Lect. Notes Comput. Sci. Eng. 66, 3--48 (2009; Zbl 1364.76151) Full Text: DOI
Beirão da Veiga, Lourenço; Manzini, Gianmarco An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems. (English) Zbl 1195.65146 Int. J. Numer. Methods Eng. 76, No. 11, 1696-1723 (2008). MSC: 65N06 65N15 76M20 74S20 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} and \textit{G. Manzini}, Int. J. Numer. Methods Eng. 76, No. 11, 1696--1723 (2008; Zbl 1195.65146) Full Text: DOI
Cangiani, Andrea; Manzini, Gianmarco Flux reconstruction and solution post-processing in mimetic finite difference methods. (English) Zbl 1169.76404 Comput. Methods Appl. Mech. Eng. 197, No. 9-12, 933-945 (2008). MSC: 76M20 76R50 PDFBibTeX XMLCite \textit{A. Cangiani} and \textit{G. Manzini}, Comput. Methods Appl. Mech. Eng. 197, No. 9--12, 933--945 (2008; Zbl 1169.76404) Full Text: DOI
Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas Multiscale mixed/mimetic methods on corner-point grids. (English) Zbl 1259.76065 Comput. Geosci. 12, No. 3, 297-315 (2008). MSC: 76S05 76M25 PDFBibTeX XMLCite \textit{J. E. Aarnes} et al., Comput. Geosci. 12, No. 3, 297--315 (2008; Zbl 1259.76065) Full Text: DOI
Natvig, Jostein R.; Lie, Knut-Andreas Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. (English) Zbl 1218.76029 J. Comput. Phys. 227, No. 24, 10108-10124 (2008). MSC: 76M10 76S05 76T99 65M60 PDFBibTeX XMLCite \textit{J. R. Natvig} and \textit{K.-A. Lie}, J. Comput. Phys. 227, No. 24, 10108--10124 (2008; Zbl 1218.76029) Full Text: DOI
Gyrya, Vitaliy; Lipnikov, Konstantin High-order mimetic finite difference method for diffusion problems on polygonal meshes. (English) Zbl 1152.65101 J. Comput. Phys. 227, No. 20, 8841-8854 (2008). MSC: 65N06 35J25 65N12 65N50 PDFBibTeX XMLCite \textit{V. Gyrya} and \textit{K. Lipnikov}, J. Comput. Phys. 227, No. 20, 8841--8854 (2008; Zbl 1152.65101) Full Text: DOI
Yuan, Guangwei; Sheng, Zhiqiang Monotone finite volume schemes for diffusion equations on polygonal meshes. (English) Zbl 1147.65069 J. Comput. Phys. 227, No. 12, 6288-6312 (2008). MSC: 65M06 35K05 65M50 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{G. Yuan} and \textit{Z. Sheng}, J. Comput. Phys. 227, No. 12, 6288--6312 (2008; Zbl 1147.65069) Full Text: DOI
Lipnikov, K.; Moulton, J. D.; Svyatskiy, D. A multilevel multiscale mimetic (M\(^3\)) method for two-phase flows in porous media. (English) Zbl 1338.76096 J. Comput. Phys. 227, No. 14, 6727-6753 (2008). MSC: 76M25 76S05 76T99 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 227, No. 14, 6727--6753 (2008; Zbl 1338.76096) Full Text: DOI
Beirão da Veiga, L. A residual based error estimator for the mimetic finite difference method. (English) Zbl 1144.65067 Numer. Math. 108, No. 3, 387-406 (2008). Reviewer: Stefan Jakobsson (Göteborg) MSC: 65N15 65N06 35J25 PDFBibTeX XMLCite \textit{L. Beirão da Veiga}, Numer. Math. 108, No. 3, 387--406 (2008; Zbl 1144.65067) Full Text: DOI
Lipnikov, K.; Shashkov, M.; Svyatskiy, D.; Vassilevski, Yu. Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. (English) Zbl 1130.65113 J. Comput. Phys. 227, No. 1, 492-512 (2007). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N50 35J25 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 227, No. 1, 492--512 (2007; Zbl 1130.65113) Full Text: DOI