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 - <p style="text-align: justify;">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.</p>