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arXiv · 2408.10227

A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids

Shangyou Zhang
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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 convergen solutions for solving the stationary Stokes equations. Numerical tests confirm the theory.

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Shangyou Zhang. 2024-08-02. A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids. https://arxiv.org/abs/2408.10227

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