Fixing a ''Bug'' in Recovery-Type A Posteriori Error Estimators

Jeffrey Ovall
(Please use for correspondence this email).

Submission date: 13. Mar. 2006
Pages: 9
paper submitted to: SIAM journal on numerical analysis
MSC-Numbers: 65N15, 65N30, 65N50
Keywords and phrases: finite elements, gradient recovery, a posteriori error estimation
Download preprint: PDF (579 kB)

Abstract:
Gradient recovery methods for \textit{a posteriori} error estimation in the finite element method are justifiably popular. They are relatively simple to implement, cheap in terms of storage and computational cost, and generally provide efficient and reliable global and local error estimates for adaptive algorithms. In this paper we highlight a difficulty that such error estimators have in the case of problems with a jumping coefficient on the diffusion term of the differential operator, explain why this difficulty exists and offer a fairly straight-forward way to fix it.