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

2024/08/02 by Zhang, Shangyou
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2408.10227

Abstract

A nonconforming P₂ finite element is constructed by enriching the conforming P₂ finite element space with seven P₂ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming P₂ finite element, combined with the discontinuous P₁ 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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