A Meshing Strategy for a Quadratic Iso-parametric FEM in Cavitation Computation in Nonlinear Elasticity

TL;DR

This paper analyzes a quadratic iso-parametric finite element method for cavitation in nonlinear elasticity, establishing error estimates, proposing a mesh strategy, and proving convergence with numerical validation.

Contribution

It introduces a meshing strategy based on error equi-distribution and proves convergence for the finite element solutions in cavitation problems.

Findings

Optimal convergence rate achieved in numerical experiments

Error estimates are established in terms of mesh parameters

Mesh distribution strategy improves solution accuracy

Abstract

The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of the mesh parameters; (2) a mesh distribution strategy based on an error equi-distribution principle is given; (3) the convergence of finite element cavity solutions is proved. Numerical experiments show that, in fact, the optimal convergence rate can be achieved by the numerical cavity solutions.