Variable Order Mixed H-Finite Element Method for Linear Elasticity with Weakly Imposed Symmetry. Ii. Affine and Curvilinear Elements in 2D

TL;DR

This paper extends the analysis of variable order mixed finite element methods for 2D linear elasticity, providing stability results for affine and curvilinear elements, supported by numerical experiments.

Contribution

It introduces stability results for affine and curvilinear elements in variable order mixed finite element methods for elasticity.

Findings

Stability results for affine elements confirmed.

Asymptotic stability for curvilinear elements established.

Numerical experiments support theoretical findings.

Abstract

We continue our study on variable order Arnold-Falk-Winther elements for 2D elasticity in context of both affine and parametric curvilinear elements. We present an $h$-stability result for affine elements, and an asymptotic stability result for curvilinear elements. Both theoretical results are confirmed with numerical experiments.