A staggered finite element cell-centered scheme for nearly incompressible elasticity on general meshes

TL;DR

This paper introduces a simple, stable, and efficient finite element cell-centered scheme for nearly incompressible elasticity problems on general meshes, utilizing a dual mesh technique to ensure stability and accuracy.

Contribution

The paper develops a novel staggered FECC scheme that guarantees stability on arbitrary meshes using dual mesh techniques, improving accuracy and computational efficiency.

Findings

The scheme satisfies the macroelement stability condition.

Numerical results demonstrate high accuracy and low computational cost.

The method is easy to implement on general meshes.

Abstract

We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh and it is proved to satisfy the "macroelement condition" [5], meaning that the stability condition is fulfilled. Numerical results show that the method, which is simple to implement, is effective in terms of accuracy and computational cost compared with other methods.