Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes
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
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A residual based error estimator for the Mimetic Finite Difference method
Numerische Mathematik
A multilevel multiscale mimetic (M3) method for two-phase flows in porous media
Journal of Computational Physics
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
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
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
Journal of Computational Physics
A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
SIAM Journal on Scientific Computing
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 Reissner–Mindlin plate bending problem
Numerische Mathematik
Equivalent projectors for virtual element methods
Computers & Mathematics with Applications
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
Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM
Computers & Mathematics with Applications
Hi-index | 0.01 |
We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. These methods are derived from the local consistency condition that is exact for polynomials of any degree $m\geq1$. The degrees of freedom are (a) solution values at the quadrature nodes of the Gauss-Lobatto formulas on each mesh edge, and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived in a mesh-dependent norm that mimics the energy norm. Numerical experiments confirm the convergence rate that is expected from the theory.