Small-stencil 3D schemes for diffusive flows in porous media

By Robert Eymard, Cindy Guichard, Raphaèle Herbin. 2012

171 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b98fc20b8b20cb69fea55636c3d47ce628bc52e9

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

VERTEX CENTRED DISCRETIZATION OF TWO-PHASE DARCY FLOWS ON GENERAL MESHES (2012, unknown): “ESAIM: PROCEEDINGS 5 Following [9], the Vertex Approximate Gradient (VAG) scheme is defined by the discrete variational formulation: find u ∈WD such that us = us for all s ∈ VD and aD(u, v) + ∫”
A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, methodology): “Examples of methods that have been proposed so far include mimetic finite differences [20, 35, 51, 52], polygonal finite element methods [58, 59], discontinuous-Galerkin finite element methods [4, 5, 9, 16, 37, 38, 40] hybridizable and hybrid high hrder methods [42, 43, 45], BEM-based FEM [56] and g”
TP or not TP, that is the question (2014, methodology): “Here, we concentrate on the finite volume scheme with two-point flux approximation, which is widely used in industry, and which we shall call the TP scheme here for short, and on the class of gradient schemes, which can be shown to include well-known schemes such as the conforming finite elements wi”
Vertex-centred discretization of multiphase compositional Darcy flows on general meshes (2012, methodology): “Let us recall the simplest one based on a conforming finite element discretization on a tetrahedral sub-mesh, and we refer to [16, 15] for two other constructions sharing the same basic features.”
A monotone nonlinear finite volume method for approximating diffusion operators on general meshes (2016, methodology): “Nowadays, besides the numerical methods that are currently used for the approximation of isotropic or anisotropic diffusion operators on rectangle, triangle (tetrahedron), or quadrilateral (hexahedron) meshes — finite difference (FD), see [1], — conformal and non-conformal finite element (FE), see [”
Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media (2014, background): “Vertex approximate gradient discretization In the spirit of [13], we consider generalised polyhedral meshes of Ω.”
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation (2014, methodology): “These methods have been studied in [13] for linear elliptic problems, and in [11] in the case of nonlinear Leray-Lions-type elliptic and parabolic problems.”