A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids
Numerical Analysis
2024-08-21 v1 Numerical Analysis
Abstract
A nonconforming finite element is constructed by enriching the conforming finite element space with seven nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming finite element, combined with the discontinuous 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 convergen solutions for solving the stationary Stokes equations. Numerical tests confirm the theory.
Keywords
Cite
@article{arxiv.2408.10227,
title = {A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids},
author = {Shangyou Zhang},
journal= {arXiv preprint arXiv:2408.10227},
year = {2024}
}