Recovery-Based Error Estimators for Diffusion Problems: Explicit Formulas
Abstract
We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e., requiring solutions of global problems with mass matrices). In this paper, we develop fully explicit recovery-based error estimators for lower order conforming, mixed, and non- conforming finite element approximations to diffusion problems with full coefficient tensor. When the diffusion coefficient is piecewise constant scalar and its distribution is local quasi-monotone, it is shown theoretically that the estimators developed in this paper are robust with respect to the size of jumps. Numerical experiments are also performed to support the theoretical results.
Cite
@article{arxiv.1407.4377,
title = {Recovery-Based Error Estimators for Diffusion Problems: Explicit Formulas},
author = {Zhiqiang Cai and Shun Zhang},
journal= {arXiv preprint arXiv:1407.4377},
year = {2014}
}