Year: 2020
Author: Xiangrong Li, Nan Qi, Weiwei Zhang, Yufeng Nie
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 236–253
Abstract
The mesh conditions of high-quality grids generated by bubble placement method (BPM) and their superconvergence properties are studied in this paper. A mesh condition that for each pair of adjacent triangles, the lengths of any two opposite edges differ only by a high order of the parameter $h$ is derived. Furthermore, superconvergence estimations are analyzed on both linear and quadratic finite elements for elliptic boundary value problems under the above mesh condition. In particular, the mesh condition is found to be applicable to many known superconvergence estimations under different types of equations. Finally, numerical examples are presented to demonstrate the superconvergence properties on BPM-based grids.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13649
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 236–253
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Bubble placement method mesh condition superconvergence estimation.