Gradient schemes: Generic tools for the numerical analysis of diffusion equations
ESAIM: M2AN, 50 3 (2016) 749-781
Published online: 2016-05-23
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Nodal discrete duality numerical scheme for nonlinear diffusion problems on general meshes
Boris Andreianov and El Houssaine QuenjelIMA Journal of Numerical Analysis 44 (3) 1597 (2024)
https://doi.org/10.1093/imanum/drad041
Biquadratic element discrete duality finite volume method for solving elliptic equations on quadrilateral mesh
Kejia Pan, Xiaoxin Wu and Yufeng XuJournal of Computational Physics 503 112857 (2024)
https://doi.org/10.1016/j.jcp.2024.112857
The gradient discretisation method for the chemical reactions of biochemical systems
Yahya Alnashri and Hasan AlzubaidiArab Journal of Mathematical Sciences 30 (1) 67 (2024)
https://doi.org/10.1108/AJMS-01-2022-0021
A Hybrid High-Order Method for a Class of Strongly Nonlinear Elliptic Boundary Value Problems
Gouranga Mallik and Thirupathi GudiJournal of Scientific Computing 98 (1) (2024)
https://doi.org/10.1007/s10915-023-02390-4
Gradient discretization of a 3D-2D-1D mixed-dimensional diffusive model with resolved interface, application to the drying of a fractured porous medium
K Brenner, Florent Chave and R MassonIMA Journal of Numerical Analysis 43 (6) 3522 (2023)
https://doi.org/10.1093/imanum/drac076
A unified analysis for reaction–diffusion models with application to the spiral waves dynamics of the Barkley model
Yahya Alnashri and Hasan AlzubaidiArabian Journal of Mathematics 12 (3) 445 (2023)
https://doi.org/10.1007/s40065-023-00423-2
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator
Jérôme Droniou, Beniamin Goldys and Kim-Ngan LeIMA Journal of Numerical Analysis 42 (2) 1143 (2022)
https://doi.org/10.1093/imanum/draa105
A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type
Thirupathi Gudi, Gouranga Mallik and Tamal PramanickSIAM Journal on Numerical Analysis 60 (4) 2318 (2022)
https://doi.org/10.1137/21M1412050
Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes
Léo Agélas, Martin Schneider, Guillaume Enchéry and Bernd FlemischIMA Journal of Numerical Analysis 42 (1) 515 (2022)
https://doi.org/10.1093/imanum/draa064
A Virtual Element Method for the Wave Equation on Curved Edges in Two Dimensions
Franco Dassi, Alessio Fumagalli, Ilario Mazzieri, Anna Scotti and Giuseppe VaccaJournal of Scientific Computing 90 (1) (2022)
https://doi.org/10.1007/s10915-021-01683-w
Convergence analysis for a nonlinear system of parabolic variational inequalities
Yahya AlnashriJournal of Inequalities and Applications 2022 (1) (2022)
https://doi.org/10.1186/s13660-022-02751-x
A Gradient Discretisation Method for Anisotropic Reaction–Diffusion Models with Applications to the Dynamics of Brain Tumors
Yahya Alnashri and Hasan AlzubaidiComputational Methods in Applied Mathematics 21 (4) 753 (2021)
https://doi.org/10.1515/cmam-2020-0081
Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations
Martin J. Gander, Laurence Halpern, Florence Hubert and Stella KrellMoroccan Journal of Pure and Applied Analysis 7 (2) 182 (2021)
https://doi.org/10.2478/mjpaa-2021-0014
Polyhedral Methods in Geosciences
Paola F. Antonietti, Chiara Facciolà, Paul Houston, et al.SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 159 (2021)
https://doi.org/10.1007/978-3-030-69363-3_5
A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores
Jean-Marc GratienJournal of Computational and Applied Mathematics 373 112614 (2020)
https://doi.org/10.1016/j.cam.2019.112614
Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids
Paola F. Antonietti, Chiara Facciolà and Marco VeraniMathematics in Engineering 2 (2) 340 (2020)
https://doi.org/10.3934/mine.2020017
Convergence of a positive nonlinear DDFV scheme for degenerate parabolic equations
El Houssaine Quenjel, Mazen Saad, Mustapha Ghilani and Marianne Bessemoulin-ChatardCalcolo 57 (2) (2020)
https://doi.org/10.1007/s10092-020-00367-5
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation
Jan Papež, Ulrich Rüde, Martin Vohralík and Barbara WohlmuthComputer Methods in Applied Mechanics and Engineering 371 113243 (2020)
https://doi.org/10.1016/j.cma.2020.113243
A Q1-finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh
Qi Hong and Jiming WuJournal of Computational and Applied Mathematics 372 112732 (2020)
https://doi.org/10.1016/j.cam.2020.112732
Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part I: Theory
Felix del Teso, Jørgen Endal and Espen R. JakobsenSIAM Journal on Numerical Analysis 57 (5) 2266 (2019)
https://doi.org/10.1137/19M1237041
Unified Convergence Analysis of Numerical Schemes for a Miscible Displacement Problem
Jérôme Droniou, Robert Eymard, Alain Prignet and Kyle S. TalbotFoundations of Computational Mathematics 19 (2) 333 (2019)
https://doi.org/10.1007/s10208-018-9387-y
Numerical analysis of a two-phase flow discrete fracture matrix model
Jérôme Droniou, Julian Hennicker and Roland MassonNumerische Mathematik 141 (1) 21 (2019)
https://doi.org/10.1007/s00211-018-0994-y
Positive control volume finite element scheme for a degenerate compressible two-phase flow in anisotropic porous media
Mustapha Ghilani, EL Houssaine Quenjel and Mazen SaadComputational Geosciences 23 (1) 55 (2019)
https://doi.org/10.1007/s10596-018-9783-z
Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids
Paola Antonietti, Marco Verani, Christian Vergara and Stefano ZoncaFinite Elements in Analysis and Design 159 1 (2019)
https://doi.org/10.1016/j.finel.2019.02.002
Comparison of finite-volume schemes for diffusion problems
Martin Schneider, Dennis Gläser, Bernd Flemisch, et al.Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 82 (2018)
https://doi.org/10.2516/ogst/2018064
SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations
S. Berrone, A. Borio and G. ManziniComputer Methods in Applied Mechanics and Engineering 340 500 (2018)
https://doi.org/10.1016/j.cma.2018.05.027
Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes
Jiangguo Liu, Simon Tavener and Zhuoran WangSIAM Journal on Scientific Computing 40 (5) B1229 (2018)
https://doi.org/10.1137/17M1145677
Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part II: Schemes and Experiments
Félix del Teso, Jørgen Endal and Espen R. JakobsenSIAM Journal on Numerical Analysis 56 (6) 3611 (2018)
https://doi.org/10.1137/18M1180748
Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods
Paola F. Antonietti, Paul Houston and Giorgio PennesiJournal of Scientific Computing 77 (3) 1339 (2018)
https://doi.org/10.1007/s10915-018-0802-y
A decoupled and positivity-preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes
Shuai Su, Qiannan Dong and Jiming WuJournal of Computational Physics 372 773 (2018)
https://doi.org/10.1016/j.jcp.2018.06.052
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows
Martin Vohralík and Soleiman YousefComputer Methods in Applied Mechanics and Engineering 331 728 (2018)
https://doi.org/10.1016/j.cma.2017.11.027
Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes
Daniele A. Di Pietro, Jérôme Droniou and Gianmarco ManziniJournal of Computational Physics 355 397 (2018)
https://doi.org/10.1016/j.jcp.2017.11.018
Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme
Jérôme Droniou and Neela NatarajIMA Journal of Numerical Analysis 38 (3) 1254 (2018)
https://doi.org/10.1093/imanum/drx028
A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem
Yahya Alnashri and Jérôme DroniouSIAM Journal on Numerical Analysis 56 (4) 2375 (2018)
https://doi.org/10.1137/16M1105517
Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method
Jérome Droniou, Neela Nataraj and Devika ShylajaComputational Methods in Applied Mathematics 18 (4) 609 (2018)
https://doi.org/10.1515/cmam-2017-0054
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
J. Droniou and R. EymardSpringer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 311 (2017)
https://doi.org/10.1007/978-3-319-57397-7_24
A posteriori error estimates for the virtual element method
Andrea Cangiani, Emmanuil H. Georgoulis, Tristan Pryer and Oliver J. SuttonNumerische Mathematik 137 (4) 857 (2017)
https://doi.org/10.1007/s00211-017-0891-9
The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences
Jérome Droniou, Neela Nataraj and Devika ShylajaSIAM Journal on Control and Optimization 55 (6) 3640 (2017)
https://doi.org/10.1137/17M1117768
1 (2017)
https://doi.org/10.1002/9781119176817.ecm2010
Convergence analysis of some first order and second order time accurate gradient schemes for semilinear second order hyperbolic equations
Abdallah BradjiNumerical Methods for Partial Differential Equations 33 (1) 5 (2017)
https://doi.org/10.1002/num.22068
Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients
G. Manzini, K. Lipnikov, J. D. Moulton and M. ShashkovSIAM Journal on Numerical Analysis 55 (6) 2956 (2017)
https://doi.org/10.1137/16M1108479
An analysis for the convergence order of gradient schemes for semilinear parabolic equations
Abdallah BradjiComputers & Mathematics with Applications 72 (5) 1287 (2016)
https://doi.org/10.1016/j.camwa.2016.06.031
Mimetic finite difference approximation of flows in fractured porous media
Paola F. Antonietti, Luca Formaggia, Anna Scotti, Marco Verani and Nicola VerzottESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 809 (2016)
https://doi.org/10.1051/m2an/2015087
Preface
L. Beirão da Veiga and A. ErnESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 633 (2016)
https://doi.org/10.1051/m2an/2016034
Gradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods
Yahya Alnashri and Jérôme DroniouComputers & Mathematics with Applications 72 (11) 2788 (2016)
https://doi.org/10.1016/j.camwa.2016.10.004