ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

A Review of Recent Advances in Discretization Methods,a PosterioriError Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences

Daniele A. Di Pietro and Martin Vohralík
Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 69 (4) 701 (2014)
DOI: 10.2516/ogst/2013158
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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Konstantin Lipnikov and Gianmarco Manzini
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 311 (2016)
DOI: 10.1007/978-3-319-41640-3_10
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An H1-conforming virtual element for Darcy and Brinkman equations

Giuseppe Vacca
Mathematical Models and Methods in Applied Sciences 28 (01) 159 (2018)
DOI: 10.1142/S0218202518500057
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Numerical Methods for PDEs

Daniele Antonio Di Pietro and Roberta Tittarelli
SEMA SIMAI Springer Series, Numerical Methods for PDEs 15 75 (2018)
DOI: 10.1007/978-3-319-94676-4_4
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A higher‐order equilibrium finite element method

K. Olesen, B. Gervang, J. N. Reddy and M. Gerritsma
International Journal for Numerical Methods in Engineering 114 (12) 1262 (2018)
DOI: 10.1002/nme.5785
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Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes

Daniele Boffi and Daniele A. Di Pietro
ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 1 (2018)
DOI: 10.1051/m2an/2017036
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Encyclopedia of Computational Mechanics Second Edition

Timothy Barth, Raphaèle Herbin and Mario Ohlberger
Encyclopedia of Computational Mechanics Second Edition 1 (2017)
DOI: 10.1002/9781119176817.ecm2010
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Virtual element methods for parabolic problems on polygonal meshes

Giuseppe Vacca and Lourenco Beirão da Veiga
Numerical Methods for Partial Differential Equations 31 (6) 2110 (2015)
DOI: 10.1002/num.21982
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A vertex-centered linearity-preserving discretization of diffusion problems on polygonal meshes

Jiming Wu, Zhiming Gao and Zihuan Dai
International Journal for Numerical Methods in Fluids 81 (3) 131 (2016)
DOI: 10.1002/fld.4178
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Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes

Jérôme Bonelle and Alexandre Ern
IMA Journal of Numerical Analysis 35 (4) 1672 (2015)
DOI: 10.1093/imanum/dru051
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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Daniele A. Di Pietro, Alexandre Ern and Simon Lemaire
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 205 (2016)
DOI: 10.1007/978-3-319-41640-3_7
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Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes

Jérôme Bonelle, Daniele A. Di Pietro and Alexandre Ern
Computer Aided Geometric Design 35-36 27 (2015)
DOI: 10.1016/j.cagd.2015.03.015
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Numerical Mathematics and Advanced Applications ENUMATH 2015

Marc Gerritsma, Jeroen Kunnen and Boudewijn de Heij
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2015 112 635 (2016)
DOI: 10.1007/978-3-319-39929-4_61
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Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains

Abhilash Sreekumar, Savvas P. Triantafyllou, François-Xavier Bécot and Fabien Chevillotte
Computer Methods in Applied Mechanics and Engineering 375 113543 (2021)
DOI: 10.1016/j.cma.2020.113543
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Jérôme Bonelle, Alexandre Ern and Riccardo Milani
323 93 (2020)
DOI: 10.1007/978-3-030-43651-3_6
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A numerical simulation model for multi-scale flow in tight oil reservoirs

Wenchao FANG, Hanqiao JIANG, Junjian LI, et al.
Petroleum Exploration and Development 44 (3) 446 (2017)
DOI: 10.1016/S1876-3804(17)30051-4
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Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes

Daniele A. Di Pietro and Alexandre Ern
IMA Journal of Numerical Analysis 37 (1) 40 (2017)
DOI: 10.1093/imanum/drw003
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New polyhedral discretisation methods applied to the Richards equation: CDO schemes in Code_Saturne

Jérôme Bonelle, Yvan Fournier and Charles Moulinec
Computers & Fluids 173 93 (2018)
DOI: 10.1016/j.compfluid.2018.03.026
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Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

Daniele A. Di Pietro, Jérôme Droniou and Francesca Rapetti
Mathematical Models and Methods in Applied Sciences 1 (2020)
DOI: 10.1142/S0218202520500372
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An edge-based scheme on polyhedral meshes for vector advection-reaction equations

Pierre Cantin and Alexandre Ern
ESAIM: Mathematical Modelling and Numerical Analysis 51 (5) 1561 (2017)
DOI: 10.1051/m2an/2016075
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$$H({\text {div}})$$ H ( div ) and $$H(\mathbf{curl})$$ H ( curl ) -conforming virtual element methods

L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo
Numerische Mathematik 133 (2) 303 (2016)
DOI: 10.1007/s00211-015-0746-1
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Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems

L. Beirão da Veiga and G. Manzini
ESAIM: Mathematical Modelling and Numerical Analysis 49 (2) 577 (2015)
DOI: 10.1051/m2an/2014047
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Finite-difference schemes for anisotropic diffusion

Bram van Es, Barry Koren and Hugo J. de Blank
Journal of Computational Physics 272 526 (2014)
DOI: 10.1016/j.jcp.2014.04.046
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Hybrid high-order methods for variable-diffusion problems on general meshes

Daniele A. Di Pietro and Alexandre Ern
Comptes Rendus Mathematique 353 (1) 31 (2015)
DOI: 10.1016/j.crma.2014.10.013
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Discrete Helmholtz–Hodge Decomposition on Polyhedral Meshes Using Compatible Discrete Operators

A. Lemoine, J.-P. Caltagirone, M. Azaïez and S. Vincent
Journal of Scientific Computing 65 (1) 34 (2015)
DOI: 10.1007/s10915-014-9952-8
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Addressing integration error for polygonal finite elements through polynomial projections: A patch test connection

Cameron Talischi and Glaucio H. Paulino
Mathematical Models and Methods in Applied Sciences 24 (08) 1701 (2014)
DOI: 10.1142/S0218202514400077
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Gradient schemes: Generic tools for the numerical analysis of diffusion equations

Jérome Droniou, Robert Eymard and Raphaèle Herbin
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 749 (2016)
DOI: 10.1051/m2an/2015079
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Geometrically defined basis functions for polyhedral elements with applications to computational electromagnetics

Lorenzo Codecasa, Ruben Specogna and Francesco Trevisan
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 677 (2016)
DOI: 10.1051/m2an/2015077
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Mixed virtual element methods for general second order elliptic problems on polygonal meshes

Lourenço Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini and Alessandro Russo
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 727 (2016)
DOI: 10.1051/m2an/2015067
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Interpolation error estimates for harmonic coordinates on polytopes

Andrew Gillette and Alexander Rand
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 651 (2016)
DOI: 10.1051/m2an/2015096
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A stress/displacement Virtual Element method for plane elasticity problems

E. Artioli, S. de Miranda, C. Lovadina and L. Patruno
Computer Methods in Applied Mechanics and Engineering 325 155 (2017)
DOI: 10.1016/j.cma.2017.06.036
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Preface

L. Beirão da Veiga and A. Ern
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 633 (2016)
DOI: 10.1051/m2an/2016034
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Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme

Jérôme Droniou and Neela Nataraj
IMA Journal of Numerical Analysis 38 (3) 1254 (2018)
DOI: 10.1093/imanum/drx028
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Numerical Methods for PDEs

Marc Gerritsma, Artur Palha, Varun Jain and Yi Zhang
SEMA SIMAI Springer Series, Numerical Methods for PDEs 15 31 (2018)
DOI: 10.1007/978-3-319-94676-4_3
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A vertex-based scheme on polyhedral meshes for advection–reaction equations with sub-mesh stabilization

Pierre Cantin, Jérôme Bonelle, Erik Burman and Alexandre Ern
Computers & Mathematics with Applications 72 (9) 2057 (2016)
DOI: 10.1016/j.camwa.2016.07.038
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A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations

A. Palha and M. Gerritsma
Journal of Computational Physics 328 200 (2017)
DOI: 10.1016/j.jcp.2016.10.009
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A discontinuous skeletal method for the viscosity-dependent Stokes problem

Daniele A. Di Pietro, Alexandre Ern, Alexander Linke and Friedhelm Schieweck
Computer Methods in Applied Mechanics and Engineering 306 175 (2016)
DOI: 10.1016/j.cma.2016.03.033
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Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions

Karol L Cascavita, Franz Chouly and Alexandre Ern
IMA Journal of Numerical Analysis 40 (4) 2189 (2020)
DOI: 10.1093/imanum/drz038
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Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods

Shuhao Cao and Long Chen
SIAM Journal on Numerical Analysis 57 (3) 1058 (2019)
DOI: 10.1137/18M1196455
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A multiscale virtual element method for the analysis of heterogeneous media

Abhilash Sreekumar, Savvas P. Triantafyllou, François‐Xavier Bécot and Fabien Chevillotte
International Journal for Numerical Methods in Engineering 121 (8) 1791 (2020)
DOI: 10.1002/nme.6287
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Hybrid High-Order Methods for the Elliptic Obstacle Problem

Matteo Cicuttin, Alexandre Ern and Thirupathi Gudi
Journal of Scientific Computing 83 (1) (2020)
DOI: 10.1007/s10915-020-01195-z
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Trefftz Finite Elements on Curvilinear Polygons

Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds and Steffen Weißer
SIAM Journal on Scientific Computing 42 (2) A1289 (2020)
DOI: 10.1137/19M1294046
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Analysis of the decoupled and positivity-preserving DDFV schemes for diffusion problems on polygonal meshes

Qiannan Dong, Shuai Su and Jiming Wu
Advances in Computational Mathematics 46 (2) (2020)
DOI: 10.1007/s10444-020-09748-4
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Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applications

Martin Ferrand and Jeffrey C. Harris
Computers & Fluids 219 104860 (2021)
DOI: 10.1016/j.compfluid.2021.104860
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Explicit geometric construction of sparse inverse mass matrices for arbitrary tetrahedral grids

Silvano Pitassi, Francesco Trevisan and Ruben Specogna
Computer Methods in Applied Mechanics and Engineering 377 113699 (2021)
DOI: 10.1016/j.cma.2021.113699
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A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows

Martin Vohralík and Soleiman Yousef
Computer Methods in Applied Mechanics and Engineering 331 728 (2018)
DOI: 10.1016/j.cma.2017.11.027
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Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods

Bernardo Cockburn, Daniele A. Di Pietro and Alexandre Ern
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 635 (2016)
DOI: 10.1051/m2an/2015051
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A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

Shuai Wang, Xudeng Hang and Guangwei Yuan
Journal of Computational Physics 350 590 (2017)
DOI: 10.1016/j.jcp.2017.08.060
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An Arbitrary-Order Discrete de Rham Complex on Polyhedral Meshes: Exactness, Poincaré Inequalities, and Consistency

Daniele A. Di Pietro and Jérôme Droniou
Foundations of Computational Mathematics (2021)
DOI: 10.1007/s10208-021-09542-8
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The role of the dual grid in low-order compatible numerical schemes on general meshes

Silvano Pitassi, Riccardo Ghiloni, Francesco Trevisan and Ruben Specogna
Journal of Computational Physics 436 110285 (2021)
DOI: 10.1016/j.jcp.2021.110285
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Artificial Compressibility Methods for the Incompressible Navier–Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes

Riccardo Milani, Jérôme Bonelle and Alexandre Ern
Computational Methods in Applied Mathematics 22 (1) 133 (2022)
DOI: 10.1515/cmam-2021-0089
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Virtual elements for sound propagation in complex poroelastic media

Abhilash Sreekumar, Savvas P. Triantafyllou and Fabien Chevillotte
Computational Mechanics 69 (1) 347 (2022)
DOI: 10.1007/s00466-021-02078-2
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A Nyström-based finite element method on polygonal elements

Akash Anand, Jeffrey S. Ovall and Steffen Weißer
Computers & Mathematics with Applications 75 (11) 3971 (2018)
DOI: 10.1016/j.camwa.2018.03.007
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Articles citing this article

Cited article:

Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes

This article has been cited by the following article(s):

A Review of Recent Advances in Discretization Methods,a PosterioriError Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

An H1-conforming virtual element for Darcy and Brinkman equations

Numerical Methods for PDEs

A higher‐order equilibrium finite element method

Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes

Encyclopedia of Computational Mechanics Second Edition

Virtual element methods for parabolic problems on polygonal meshes

A vertex-centered linearity-preserving discretization of diffusion problems on polygonal meshes

Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes

Numerical Mathematics and Advanced Applications ENUMATH 2015

Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains

A numerical simulation model for multi-scale flow in tight oil reservoirs

Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes

New polyhedral discretisation methods applied to the Richards equation: CDO schemes in Code_Saturne

Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

An edge-based scheme on polyhedral meshes for vector advection-reaction equations

$$H({\text {div}})$$ H ( div ) and $$H(\mathbf{curl})$$ H ( curl ) -conforming virtual element methods

Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems

Finite-difference schemes for anisotropic diffusion

Hybrid high-order methods for variable-diffusion problems on general meshes

Discrete Helmholtz–Hodge Decomposition on Polyhedral Meshes Using Compatible Discrete Operators

Addressing integration error for polygonal finite elements through polynomial projections: A patch test connection

Gradient schemes: Generic tools for the numerical analysis of diffusion equations

Geometrically defined basis functions for polyhedral elements with applications to computational electromagnetics

Mixed virtual element methods for general second order elliptic problems on polygonal meshes

Interpolation error estimates for harmonic coordinates on polytopes

A stress/displacement Virtual Element method for plane elasticity problems

Preface

Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme

Numerical Methods for PDEs

A vertex-based scheme on polyhedral meshes for advection–reaction equations with sub-mesh stabilization

A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations

A discontinuous skeletal method for the viscosity-dependent Stokes problem

Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions

Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods

A multiscale virtual element method for the analysis of heterogeneous media

Hybrid High-Order Methods for the Elliptic Obstacle Problem

Trefftz Finite Elements on Curvilinear Polygons

Analysis of the decoupled and positivity-preserving DDFV schemes for diffusion problems on polygonal meshes

Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applications

Explicit geometric construction of sparse inverse mass matrices for arbitrary tetrahedral grids

A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows

Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods

A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

An Arbitrary-Order Discrete de Rham Complex on Polyhedral Meshes: Exactness, Poincaré Inequalities, and Consistency

The role of the dual grid in low-order compatible numerical schemes on general meshes

Artificial Compressibility Methods for the Incompressible Navier–Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes

Virtual elements for sound propagation in complex poroelastic media

A Nyström-based finite element method on polygonal elements