Year: 2022
Author: Xinjiang Chen, Yanqiu Wang
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 4 : pp. 624–648
Abstract
In this paper, we construct an $H^1$-conforming quadratic finite element on convex polygonal meshes using the generalized barycentric coordinates. The element has optimal approximation rates. Using this quadratic element, two stable discretizations for the Stokes equations are developed, which can be viewed as the extensions of the $P_2$-$P_0$ and the $Q_2$-(discontinuous)$P_1$ elements, respectively, to polygonal meshes. Numerical results are presented, which support our theoretical claims.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2101-m2020-0234
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 4 : pp. 624–648
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Quadratic finite element method Stokes equations Generalized barycentric coordinates.