A residual based error estimator for the Mimetic Finite Difference method

Authors:
L. Beirão da Veiga
Affiliations:
Dipartimento di Matematica “F. Enriques”, Via Saldini 50, 20133, Milano, Italy
Venue:
Numerische Mathematik
Year:
2007

Citing 0
Cited 10

Mimetic finite difference method for the Stokes problem on polygonal meshes

Journal of Computational Physics
A new set of basis functions for the discrete geometric approach

Journal of Computational Physics
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes

Journal of Computational Physics
Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems

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
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

Quantified Score

Hi-index	0.03

Visualization

Abstract

We present a local error indicator for the Mimetic Finite Difference method for diffusion-type problems on polyhedral meshes. Under essentially the same general hypotheses used in (SIAM J. Numer. Anal. 43:1872–1896, 2005) to show the convergence of the method, we prove the global reliability and local efficiency of the proposed estimator.