A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations

Authors

  • Xinjiang Chen Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
  • Yanqiu Wang Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

DOI:

https://doi.org/10.4208/jcm.2101-m2020-0234

Keywords:

Quadratic finite element method, Stokes equations, Generalized barycentric coordinates.

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.

Downloads

Published

2022-10-06

Abstract View

  • 37575

Pdf View

  • 3163

Issue

Vol. 40 No. 4 (2022)

Section

Articles

How to Cite

A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations. (2022). Journal of Computational Mathematics, 40(4), 624-648. https://doi.org/10.4208/jcm.2101-m2020-0234