A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

TL;DR

This paper introduces a new family of stable mixed finite elements for linear elasticity on tetrahedral grids, using symmetric polynomial tensors for stress and polynomial vectors for displacement, applicable for all polynomial degrees k≥4.

Contribution

The paper develops a novel family of symmetric mixed finite elements for linear elasticity on tetrahedral grids, extending the applicability to all polynomial degrees k≥4.

Findings

Numerical tests confirm stability and accuracy.

The method is applicable for all polynomial degrees k≥4.

Abstract

A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed, where the stress is approximated by symmetric $H(\d)$-$P_k$ polynomial tensors and the displacement is approximated by $C^{-1}$-$P_{k-1}$ polynomial vectors, for all $k\ge 4$. Numerical tests are provided.