Year: 1989
Author: Chuan-Miao Chen, Qun Lin
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 3 : pp. 227–233
Abstract
Recently, the Richardson extrapolation for the elliptic Ritz projection with linear triangular elements on a general convex polygonal domain was discussed by Lin and Lu. We go back in this note to the simplest case, i.e. the bilinear rectangular elements on a rectangular domain which is a parallel case of the one-triangle model in the early work of Lin and Liu. We find that the finite element argument for the Richardson extrapolation with an accuracy of $O(h^4)$ needs only the regularity of $H^{4,\infty}$ for the solution $u$ but the finite difference argument for extrapolation with $O(h^{s+\alpha})$ accuracy needs $u\in C^{5+\alpha}(0＜\alpha＜1)$. Moreover, a formula is suggested to guarantee the extrapolation of $O(h^4)$ accuracy at fine gridpoints as well as at coarse gridpoints.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1989-JCM-9473
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 3 : pp. 227–233
Published online: 1989-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 7