Superconvergence of new mixed finite element spaces

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Hyon, YunKyong¹  Kwak, Do Young² 

[1] Univ Minnesota, Inst Math & Its Applicat, Minneapolis, MN 55455 USA

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

关键词: Mixed finite element method;    Superconvergence;    Optimal order;    Post-processing;   

DOI  :  10.1016/j.cam.2011.03.022

来源: Elsevier

【 摘 要 】

In this paper we prove some superconvergence of a new family of mixed finite element spaces of higher order which we introduced in [ETNA, Vol. 37, pp. 189-201, 2010]. Among all the mixed finite element spaces having an optimal order of convergence on quadrilateral grids, this space has the smallest unknowns. However, the scalar variable is only suboptimal in general; thus we have employed a post-processing technique for the scalar variable. As a byproduct, we have obtained a superconvergence on a rectangular grid. The superconvergence of a velocity variable naturally holds and can be shown by a minor modification of existing theory, but that of a scalar variable requires a new technique, especially for k = 1. Numerical experiments are provided to support the theory. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free