Thursday, Mar 1, 2018 - 3:30pm - Allen 14
Robust a posteriori error analytic techniques for elliptic singularly perturbed problem
Dr. Shaohong Du, Mathematics, Chongqing Jiaotong University
Title: Robust a posteriori error analytic techniques for elliptic singularly perturbed problem
Abstract: In this talk, we first consider the second order elliptic singularly perturbed problem. We introduce a novel dual norm, under which robust residual-type a posteriori error estimator is developed and analyzed. The error estimator is proven to be robust with respect to the singularly perturbed parameter. Next, we develop some robust recovery-based a posteriori error estimators for SUPG method in the new dual norm. The flux is recovered through either the local averaging or the global (weighted) L^2 projection in H(div) conforming finite element spaces. Based on the H(div) recovered flux, we introduce a stabilization recovery procedure and develop completely robust a posteriori error estimator. Finally, for fourth order elliptic singularly perturbed problems with two kinds of boundary conditions, we present a measure of the error for its mixed finite element methods, and develop an analytic technique on a posteriori error estimates to obtain robust residual-based a posteriori estimator in this size. Numerical experiments are reported to support our theoretical results and to show the competitive behavior of the proposed a posteriori estimators.