Adaptive control of local errors for elliptic problems using weighted Sobolev norms

Abstract

We develop an a posteriori error estimator which focuses on the local H1 error on a region of interest. The estimator bounds a weighted Sobolev norm of the error and is efficient up to oscillation terms. The new idea is very simple and applies to a large class of problems. An adaptive method guided by this estimator is implemented and compared to other local estimators, showing an excellent performance. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1266–1282, 2017.