English

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

Numerical Analysis 2024-08-21 v1 Numerical Analysis

Abstract

A nonconforming P2P_2 finite element is constructed by enriching the conforming P2P_2 finite element space with seven P2P_2 nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming P2P_2 finite element, combined with the discontinuous P1P_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.

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}
}