A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis

DOI10.1016/j.crma.2007.01.024zbMath1112.65120OpenAlexW1995848272MaRDI QIDQ876111

Robert Eymard, Raphaèle Herbin, Thierry Gallouet

Publication date: 16 April 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2007.01.024

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient, Convergence analysis of the high-order mimetic finite difference method, Convergence of a Cell-Centered Finite Volume Discretization for Linear Elasticity, Model reduction and discretization using hybrid finite volumes for flow in porous media containing faults, Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology, A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS, A reconstruction algorithm with flexible stencils for anisotropic diffusion equations on 2D skewed meshes, A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures, A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids, A conservative network element method for diffusion-advection-reaction problems, Unnamed Item, Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system, Discrete duality finite volume scheme for a generalized Joule heating problem, On the coupling of finite volume and discontinuous Galerkin method for elliptic problems, Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems, Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes., Convergence analysis on unstructured meshes of a DDFV method for flow problems with full Neumann boundary conditions, Combined mixed finite element and nonconforming finite volume methods for flow and transport in porous media, DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS, Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes, Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods, Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces, Finite volume approximation of a diffusion-dissolution model and application to nuclear waste storage, Algebraically stabilized Lagrange multiplier method for frictional contact mechanics with hydraulically active fractures, Mimetic finite difference method for the Stokes problem on polygonal meshes, Local flux mimetic finite difference methods, A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media, The cell functional minimization scheme for the anisotropic diffusion problems on arbitrary polygonal grids, Some multiple flow direction algorithms for overland flow on general meshes, Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes, Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media

Cites Work