Mixed hp-finite element method for linear elasticity with weakly imposed symmetry III: Stability analysis in 3D

TL;DR

This paper extends Arnold-Falk-Winther elements to 3D linear elasticity with variable mesh element orders, providing a stability analysis for h-convergence despite complex interpolation modifications.

Contribution

It generalizes 3D elasticity elements to variable order meshes and offers a stability analysis for h-convergence with modified interpolation operators.

Findings

Successfully generalized Arnold-Falk-Winther elements to 3D

Provided stability analysis for variable order meshes

Focused on h-convergence stability

Abstract

The paper presents a generalization of Arnold-Falk-Winther elements for three dimensional linear elasticity, to meshes with elements of variable order. The generalization is straightforward but the stability analysis involves a non-trivial modification of involved interpolation operators. The analysis addresses only the h-convergence.