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

https://doi.org/10.1093/imanum/drx028
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/num.20333openalex-snapshot
Study of the mixed finite volume method for Stokes and Navier‐Stokes equations
inferredcites →https://doi.org/10.1002/zamm.201200206openalex-snapshot
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation
inferredcites →https://doi.org/10.1006/jcph.1998.6150openalex-snapshot
A New Formulation of the Mixed Finite Element Method for Solving Elliptic and Parabolic PDE with Triangular Elements
inferredcites →https://doi.org/10.1007/978-0-387-75934-0openalex-snapshot
The Mathematical Theory of Finite Element Methods
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The Mimetic Finite Difference Method for Elliptic Problems
inferredcites →https://doi.org/10.1007/978-3-319-79042-8openalex-snapshot
The Gradient Discretisation Method
inferredcites →https://doi.org/10.1007/bf02575912openalex-snapshot
Decentrage et elements finis mixtes pour les equations de diffusion-convection
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A mixed finite volume scheme for anisotropic diffusion problems on any grid
inferredcites →https://doi.org/10.1007/s00211-014-0636-yopenalex-snapshot
Gradient schemes for linear and non-linear elasticity equations
inferredcites →https://doi.org/10.1007/s00211-015-0733-6openalex-snapshot
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
inferredcites →https://doi.org/10.1016/j.cma.2007.09.019openalex-snapshot
Flux reconstruction and solution post-processing in mimetic finite difference methods
inferredcites →https://doi.org/10.1016/j.jcp.2013.07.031openalex-snapshot
Mimetic finite difference method
inferredcites →https://doi.org/10.1016/s0045-7825(02)00578-9openalex-snapshot
On the finite volume reformulation of the mixed finite element method for elliptic and parabolic PDE on triangles
inferredcites →https://doi.org/10.1016/s1290-0729(00)00276-3openalex-snapshot
A finite volume method to solve the Navier–Stokes equations for incompressible flows on unstructured meshes
inferredcites →https://doi.org/10.1016/s1570-8659(00)07005-8openalex-snapshot
Finite volume methods
inferredcites →https://doi.org/10.1029/96wr00566openalex-snapshot
Reply [to “Comment on ‘Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?’ by R. Mosé, P. Siegel, P. Ackerer, and G. Chavent”]
inferredcites →https://doi.org/10.1029/96wr00567openalex-snapshot
Comment on “Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?” by R. Mosé, P. Siegel, P. Ackerer, and G. Chavent
inferredcites →https://doi.org/10.1051/m2an/2010068openalex-snapshot
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
inferredcites →https://doi.org/10.1051/m2an/2011040openalex-snapshot
Small-stencil 3D schemes for diffusive flows in porous media
inferredcites →https://doi.org/10.1051/m2an/2013104openalex-snapshot
Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes
inferredcites →https://doi.org/10.1051/m2an/2013104/pdfopenalex-snapshot
Analysis of Compatible Discrete Operator Schemes for Elliptic Problems on Polyhedral Meshes
inferredcites →https://doi.org/10.1051/m2an/2015079openalex-snapshot
Gradient schemes: Generic tools for the numerical analysis of diffusion equations
inferredcites →https://doi.org/10.1051/m2an/2016033openalex-snapshot
A generalized Mimetic Finite Difference method and Two-Point Flux schemes over Voronoi diagrams
inferredcites →https://doi.org/10.1051/m2an:2005047openalex-snapshot
A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
inferredcites →https://doi.org/10.1093/imanum/drn084openalex-snapshot
Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
inferredcites →https://doi.org/10.1093/imanum/drv061openalex-snapshot
Gradient Schemes for Stokes problem
inferredcites →https://doi.org/10.1142/s0218202505000832openalex-snapshot
A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
inferredcites →https://doi.org/10.1142/s0218202510004222openalex-snapshot
A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS
inferredcites →https://doi.org/10.1142/s0218202512500613openalex-snapshot
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
inferredcites →https://doi.org/10.1142/s0218202513500358openalex-snapshot
GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS
inferredcites →https://doi.org/10.1142/s0218202514400041openalex-snapshot
Finite volume schemes for diffusion equations: Introduction to and review of modern methods
inferredcites →https://doi.org/10.1145/87252.88076openalex-snapshot
A personal retrospection of reservoir simulation
inferredcites →https://doi.org/10.1515/cmam-2014-0018openalex-snapshot
An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators
inferredcites →https://doi.org/10.70675/899bf521z4b7ez4903zb907z62b43ccbdd8aopenalex-snapshot
Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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inferred← citeshttps://doi.org/10.1002/num.22460openalex-snapshot
Improved L2 and H1 error estimates for the Hessian discretization method
inferred← citeshttps://doi.org/10.1002/oca.3135openalex-snapshot
Numerical analysis of optimal control problems governed by fourth‐order linear elliptic equations using the Hessian discretization method
inferred← citeshttps://doi.org/10.1007/978-3-030-37203-3openalex-snapshot
The Hybrid High-Order Method for Polytopal Meshes
inferred← citeshttps://doi.org/10.1007/978-3-030-37203-3_5openalex-snapshot
Variations and Comparison with Other Methods
inferred← citeshttps://doi.org/10.1007/978-3-030-69363-3_1openalex-snapshot
Non-conforming Finite Elements on Polytopal Meshes
inferred← citeshttps://doi.org/10.1007/978-3-319-57397-7_24openalex-snapshot
The Asymmetric Gradient Discretisation Method
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Numerical Scheme for Regularised Riemannian Mean Curvature Flow Equation
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inferred← citeshttps://doi.org/10.1016/j.cam.2026.117546openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.jcp.2019.108876openalex-snapshot
Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling
inferred← citeshttps://doi.org/10.1016/j.jcp.2022.111464openalex-snapshot
Parameter-Robust Methods for the Biot-Stokes Interfacial Coupling Without Lagrange Multipliers
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inferred← citeshttps://doi.org/10.1016/j.rinam.2023.100379openalex-snapshot
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inferred← citeshttps://doi.org/10.1051/m2an/2021044openalex-snapshot
Error estimate of the non-intrusive reduced basis method with finite volume schemes
inferred← citeshttps://doi.org/10.1090/mcom/4033openalex-snapshot
Optimal error bounds for the two-point flux approximation finite volume scheme
inferred← citeshttps://doi.org/10.1093/imanum/drad087openalex-snapshot
Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes
inferred← citeshttps://doi.org/10.1137/16m1105517openalex-snapshot
A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem
inferred← citeshttps://doi.org/10.1137/20m1316093openalex-snapshot
A Convergent Entropy Diminishing Finite Volume Scheme for a Cross-Diffusion System
inferred← citeshttps://doi.org/10.1137/21m1452974openalex-snapshot
Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form
inferred← citeshttps://doi.org/10.1515/cmam-2017-0054openalex-snapshot
Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method
inferred← citeshttps://doi.org/10.1515/cmam-2023-0009openalex-snapshot
A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System
inferred← citeshttps://doi.org/10.2139/ssrn.5503822openalex-snapshot
ERROR ESTIMATES FOR NUMERICAL APPROXIMATIONS OF A NONLINEAR GRADIENT FLOW MODEL
inferred← citeshttps://doi.org/10.2478/tmmp-2018-0025openalex-snapshot
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inferred← citeshttps://doi.org/10.48550/arxiv.1811.05429openalex-snapshot
Improved $L^2$ and $H^1$ error estimates for the Hessian discretisation method
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