Optimal adaptive grids of least-squares finite element methods in two spatial dimensions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article; Proceedings Paper

Chang, Shin-Perng²  Chen, Tsu-Fen¹ 

[1] Natl Chung Cheng Univ, Dept Math, Chiayi, Taiwan

[2] Hsuan Chuang Univ, Dept Appl Math, Hsinchu, Taiwan

关键词: Least-squares finite element method;    Convection-diffusion problems;    Mesh redistribution;    Optimal grids;   

DOI  :  10.1016/j.cam.2011.01.028

来源: Elsevier

【 摘 要 】

This article concerns a procedure to generate optimal adaptive grids for convection dominated problems in two spatial dimensions based on least-squares finite element approximations. The procedure extends a one dimensional equidistribution principle which minimizes the interpolation error in some norms. The idea is to select two directions which can reflect the physics of the problems and then apply the one dimensional equidistribution principle to the chosen directions. Model problems considered are the two dimensional convection-diffusion problems where boundary and interior layers occur. Numerical results of model problems illustrating the efficiency of the proposed scheme are presented. In addition, to avoid skewed mesh in the optimal grids generated by the algorithm, an unstructured local mesh smoothing will be considered in the least-squares approximations. Comparisons with the Gakerkin finite element method will also be provided. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free