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An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems
Author(s) -
Beirão da Veiga Lourenço,
Manzini Gianmarco
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2377
Subject(s) - polygon mesh , estimator , a priori and a posteriori , mathematics , finite element method , approximations of π , elliptic curve , finite difference , mathematical analysis , geometry , physics , philosophy , statistics , epistemology , thermodynamics
We present an a posteriori error indicator for the mimetic finite difference approximation of elliptic problems in the mixed form. We show that this estimator is reliable and efficient with respect to an energy‐type error comprising both flux and pressure. Its performance is investigated by numerically solving the diffusion equation on computational domains with different shapes, different permeability tensors, and different types of computational meshes. Copyright © 2008 John Wiley & Sons, Ltd.