A posteriori error estimators for the first-order least-squares finite element method

Authors:
JaEun Ku;Eun-Jae Park
Affiliations:
Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences Building, Stillwater, OK 74078-1058, United States;Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we propose a posteriori error estimators for certain quantities of interest for a first-order least-squares finite element method. In particular, we propose an a posteriori error estimator for when one is interested in @?@s-@s"h@?"0 where @s=-A@?u. Our a posteriori error estimators are obtained by assigning proper weight (in terms of local mesh size h"T) to the terms of the least-squares functional. An a posteriori error analysis yields reliable and efficient estimates based on residuals. Numerical examples are presented to show the effectivity of our error estimators.