Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
A tensor artificial viscosity using a mimetic finite difference algorithm
Journal of Computational Physics
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
Constitutive equations for discrete electromagnetic problems over polyhedral grids
Journal of Computational Physics
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
Convergence analysis of the high-order mimetic finite difference method
Numerische Mathematik
A new set of basis functions for the discrete geometric approach
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
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme
Journal of Computational Physics
Mimetic Discretizations of Elliptic Control Problems
Journal of Scientific Computing
Numerical results for mimetic discretization of Reissner---Mindlin plate problems
Calcolo: a quarterly on numerical analysis and theory of computation
Mimetic finite difference method
Journal of Computational Physics
Mimetic scalar products of discrete differential forms
Journal of Computational Physics
Hi-index | 31.48 |
Various approaches to extend finite element methods to non-traditional elements (general polygons, pyramids, polyhedra, etc.) have been developed over the last decade. The construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis. The mimetic finite difference (MFD) method works on general polygonal meshes and has many similarities with low-order finite element methods. Both schemes try to preserve the fundamental properties of the underlying physical and mathematical models. The essential difference between the two schemes is that the MFD method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices. Since no extension of basis functions inside the mesh elements is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we present a new MFD method for the Stokes problem on arbitrary polygonal meshes and analyze its stability. The method is developed for the general case of tensor coefficients, which allows us to apply it to a linear elasticity problem, as well. Numerical experiments show, for the velocity variable, second-order convergence in a discrete L^2 norm and first-order convergence in a discrete H^1 norm. For the pressure variable, first-order convergence is shown in the L^2 norm.