Mimetic Finite Difference Methods for Diffusion Equations

By James M. Hyman, J. Morel, Mikhail Yu. Shashkov, S. Steinberg. 2002

155 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d789807fc0533ea707ed7ee8a2b60ab34a1b464f

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Relationships among some locally conservative discretization methods which handle discontinuous coefficients (2004, methodology): “In the special issue cited above, the papers about these or conceptually similar methods were as follows: CVMFEM [14], SOM [15], ECCFDM [16], MPFA [11, 17, 18, 19, 20].”
SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications (2015, methodology): “In SIMPEG, we have implemented a staggered mimetic finite volume approach (Hyman and Shashkov, 1999; Hyman et al., 2002).”
A Mimetic discretization method for linear elasticity (2010, unknown): “Although the MFD method has been applied to a variety of problems, such as electromagnetics and gas dynamics, the main benchmark of development and application has been the diffusion problem, see for example [11,12,24–29].”
Mimetic finite difference method (2014, background): “…the mimetic discretizations are applied to a wide range of problem: diffusion equations with strongly discontinuous anisotropic coefficients, [141] [143] [240]; Maxwell's equations and equations of a magnetic diffusion, [148] [150]; equations of the Lagrangian hydrodynamics on general…”
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes (2005, methodology): “In the context of the local MFD method [13], and taking for simplicity K̃ = I, condition (5.”
A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES (2005, methodology): “The mimetic finite difference (MFD) method [1] has been successfully employed for solving this problem on simplicial, quadrilateral, hexahedral, and unstructured polygonal and polyhedral meshes in both Cartesian and cylindrical coordinate systems.”
Challenges and Prospects in Ocean Circulation Models (2019, background): “laws, solution symmetries, and the fundamental identities and theorems of vector and tensor calculus–thus mimetic methods frequently assure consistency (Hyman et al., 2002).”