The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient

DOI10.1016/j.jcp.2015.10.031zbMath1349.65315OpenAlexW1879538256MaRDI QIDQ2374916

J. David Moulton, Mikhail J. Shashkov, Gianmarco Manzini, Konstantin N. Lipnikov

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.10.031

zbMATH Keywords

mimetic finite differencescompatible discretizationselliptic and parabolic problemsunstructured polygonal meshes

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods for boundary value problems involving PDEs (65N06)

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Cites Work

• Unnamed Item
• Mimetic finite difference method
• A mixed finite volume scheme for anisotropic diffusion problems on any grid
• A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis
• Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes.
• A finite volume method for the approximation of diffusion operators on distorted meshes
• The mimetic finite difference method for elliptic problems
• Basic principles of mixed Virtual Element Methods
• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
• Convergence of the iterative process for the quasilinear heat transfer equation
• Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry
• CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS
• M-Adaptation in the mimetic finite difference method
• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES

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