A Simple Approach to Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Problems
Numerical Analysis
2019-06-26 v1
Abstract
A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The flux reconstruction is based on simple, independent post-processing operations over patches of elements in conjunction with standard Raviart--Thomas vector fields and gives upper bounds even in cases where Galerkin orthogonality might be violated. If Galerkin orthogonality holds, we prove that the corresponding local error indicators are locally efficient and robust with respect to any mesh size and any size of the reaction coefficient, including the singularly perturbed limit.
Cite
@article{arxiv.1812.07972,
title = {A Simple Approach to Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Problems},
author = {Mark Ainsworth and Tomas Vejchodsky},
journal= {arXiv preprint arXiv:1812.07972},
year = {2019}
}