A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations

A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations

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.

Author Details

Xinjiang Chen

Yanqiu Wang