A family of edge-centered finite volume schemes for heterogeneous and anisotropic diffusion problems on unstructured meshes

DOI10.1016/j.camwa.2023.06.030MaRDI QIDQ6052324

Ziqi Liu, Shuai Miao, Zhimin Zhang

Publication date: 21 September 2023

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

diffusion equationunstructured meshedge-centered schemesymmetry and coercivity

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06) Finite volume methods for boundary value problems involving PDEs (65N08)

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Cites Work

• Unnamed Item
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• Mimetic finite difference method
• Local flux mimetic finite difference methods
• A finite volume method for the approximation of diffusion operators on distorted meshes
• A cell-centered multipoint flux approximation method with a diamond stencil coupled with a higher order finite volume method for the simulation of oil-water displacements in heterogeneous and anisotropic petroleum reservoirs
• Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
• A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions
• An introduction to multipoint flux approximations for quadrilateral grids
• Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids
• Analysis of the decoupled and positivity-preserving DDFV schemes for diffusion problems on polygonal meshes
• A second-order face-centred finite volume method for elliptic problems
• A nonlinear correction scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes
• A discrete calculus analysis of the Keller box scheme and a generalization of the method to arbitrary meshes
• Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes. (Schéma volumes finis monotone pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés).
• A non-oscillatory face-centred finite volume method for compressible flows
• An interpolation-free cell-centered discretization of the heterogeneous and anisotropic diffusion problems on polygonal meshes
• Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes
• Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
• Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods
• Finite volume schemes for diffusion equations: Introduction to and review of modern methods
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES