Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A tensor artificial viscosity using a mimetic finite difference algorithm
Journal of Computational Physics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
SIAM Journal on Matrix Analysis and Applications
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Mimetic finite difference method for the Stokes problem on polygonal meshes
Journal of Computational Physics
Journal of Computational Physics
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
Journal of Computational Physics
The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
Journal of Computational Physics
Journal of Computational Physics
Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
SIAM Journal on Scientific Computing
Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes
SIAM Journal on Numerical Analysis
Journal of Computational Physics
An improved monotone finite volume scheme for diffusion equation on polygonal meshes
Journal of Computational Physics
Equivalent projectors for virtual element methods
Computers & Mathematics with Applications
Mimetic finite difference method
Journal of Computational Physics
Mimetic scalar products of discrete differential forms
Journal of Computational Physics
Hi-index | 31.49 |
The mimetic finite difference (MFD) methods mimic important properties of physical and mathematical models. As a result, conservation laws, solution symmetries, and the fundamental identities of the vector and tensor calculus are held for discrete models. The MFD methods retain these attractive properties for full tensor coefficients and arbitrary polygonal meshes which may include non-convex and degenerate elements. The existing MFD methods for solving diffusion-type problems are second-order accurate for the conservative variable (temperature, pressure, energy, etc.) and only first-order accurate for its flux. We developed new high-order MFD methods which are second-order accurate for both scalar and vector variables. The second-order convergence rates are demonstrated with a few numerical examples on randomly perturbed quadrilateral and polygonal meshes.