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 ||σ-σh||0 where σ=-A∇u. Our a posteriori error estimators are obtained by assigning proper weight (in terms of local mesh size hT) 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.
Bibliographical noteFunding Information:
The research of EJP was supported in part by the Korea Research Foundation KRF-2007-314-C00084 and the WCU program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( R31-2008-000-10049-0 ).
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics