Multipoint stress mixed finite element methods for the linear Cosserat equations

TL;DR

This paper introduces mixed finite element methods for Cosserat materials that simplify the system by eliminating certain stress variables, demonstrating stability, convergence, and higher order accuracy through theoretical analysis and numerical experiments.

Contribution

It proposes four new mixed finite element variants for Cosserat equations that reduce system complexity and prove stability and convergence.

Findings

Methods are stable and convergent as shown by a priori estimates.

Numerical experiments confirm theoretical convergence and higher order accuracy.

The approach effectively reduces the number of variables in the system.

Abstract

We propose mixed finite element methods for Cosserat materials that use suitable quadrature rules to eliminate the Cauchy and coupled stress variables locally. The reduced system consists of only the displacement and rotation variables. Four variants are proposed for which we show stability and convergence using a priori estimates. Numerical experiments verify the theoretical findings and higher order convergence is observed in some variables.