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Volume 40, Issue 4
A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations

Xinjiang Chen & Yanqiu Wang

DOI: 10.4208/jcm.2101-m2020-0234

J. Comp. Math., 40 (2022), pp. 624-648.

Published online: 2022-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N38, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

554166448@qq.com (Xinjiang Chen)

yqwang@njnu.edu.cn (Yanqiu Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-624, author = {Chen , Xinjiang and Wang , Yanqiu}, title = {A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2101-m2020-0234}, url = {http://global-sci.org/intro/article_detail/jcm/20504.html} }
TY - JOUR T1 - A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations AU - Chen , Xinjiang AU - Wang , Yanqiu JO - Journal of Computational Mathematics VL - 4 SP - 624 EP - 648 PY - 2022 DA - 2022/04 SN - 40 DO - http://doi.org/10.4208/jcm.2101-m2020-0234 UR - https://global-sci.org/intro/article_detail/jcm/20504.html KW - Quadratic finite element method, Stokes equations, Generalized barycentric coordinates. AB -

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.

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