Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
A tensor artificial viscosity using a mimetic finite difference algorithm
Journal of Computational Physics
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
Journal of Computational Physics
Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals
SIAM Journal on Numerical Analysis
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A mixed finite volume scheme for anisotropic diffusion problems on any grid
Numerische Mathematik
A residual based error estimator for the Mimetic Finite Difference method
Numerische Mathematik
High-order mimetic finite difference method for diffusion problems on polygonal meshes
Journal of Computational Physics
A Higher-Order Formulation of the Mimetic Finite Difference Method
SIAM Journal on Scientific Computing
Local flux mimetic finite difference methods
Numerische Mathematik
Mimetic finite difference method for the Stokes problem on polygonal meshes
Journal of Computational Physics
Convergence analysis of the high-order mimetic finite difference method
Numerische Mathematik
Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems
SIAM Journal on Numerical Analysis
The Discrete Duality Finite Volume Method for Convection-diffusion Problems
SIAM Journal on Numerical Analysis
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A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The mimetic discretization methodology can be understood as a generalization of the finite element method to meshes with general polygons/polyhedrons. In this paper, the mimetic generalization of the unstable $P_1-P_0$ (and the “conditionally stable” $Q1-P0$) finite element is shown to be fully stable when applied to a large range of polygonal meshes. Moreover, we show how to stabilize the remaining cases by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments.