A nodal type polynomial finite element exact sequence over quadrilaterals
Xinchen Zhou, Zhaoliang Meng, Xin Fan, Zhongxuan Luo
TL;DR
This paper introduces two new 12-DoF nodal nonconforming finite elements for convex quadrilaterals, forming part of an exact sequence, tailored for specific PDEs with numerical validation.
Contribution
It presents novel finite elements with polynomial shape functions that form an exact sequence over quadrilaterals, suitable for elliptic and Brinkman problems.
Findings
Elements are of 12 DoFs with polynomial shape functions
Numerical examples demonstrate effectiveness
Suitable for elliptic and Brinkman PDEs
Abstract
This work proposes two nodal type nonconforming finite elements over convex quadrilaterals, which are parts of a finite element exact sequence. Both elements are of 12 degrees of freedom (DoFs) with polynomial shape function spaces selected. The first one is designed for fourth order elliptic singular perturbation problems, and the other works for Brinkman problems. Numerical examples are also provided.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Electromagnetic Scattering and Analysis · Differential Equations and Numerical Methods