Year: 2025
Author: Shangyou Zhang
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 4 : pp. 1259–1274
Abstract
A nonconforming $P_2$ finite element is constructed by enriching the conforming $P_2$ finite element space with seven $P_2$ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming $P_2$ finite element, combined with the discontinuous $P_1$ finite element on general tetrahedral grids, is inf-sup stable for solving the Stokes equations. Consequently, such a mixed finite element method produces optimal-order convergent solutions for solving the stationary Stokes equations. Numerical tests confirm the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0316
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 4 : pp. 1259–1274
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Quadratic finite element nonconforming finite element mixed finite element Stokes equations tetrahedral grid.