@Article{JCM-7-3,
author = {Chuan-Miao, Chen and Qun, Lin},
title = {Extrapolation of Finite Element Approximation in a Rectangular Domain},
journal = {Journal of Computational Mathematics},
year = {1989},
volume = {7},
number = {3},
pages = {227--233},
abstract = {<p style="text-align: justify;">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. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1989-JCM-9473},
url = {https://global-sci.com/article/86106/extrapolation-of-finite-element-approximation-in-a-rectangular-domain}
}