A remark on least-squares mixed element methods for reaction-diffusion problems

Authors:
Hongxing Rui;Seokchan Kim;Sang Dong Kim
Affiliations:
School of Mathematics and System Science, Shandong University, Jinan 250100, Shandong, China;Department of Applied Mathematics, Changwon National University, Changwon 641-773, South Korea;Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, we propose a least-squares mixed element procedure for a reaction-diffusion problem based on the first-order system. By selecting the least-squares functional properly, the resulting procedure can be split into two independent symmetric positive definite schemes, one of which is for the unknown variable and the other of which is for the unknown flux variable, which lead to the optimal order H^1(@W) and L^2(@W) norm error estimates for the primal unknown and optimal H(div;@W) norm error estimate for the unknown flux. Finally, we give some numerical examples.