Using curved meshes to derive a priori error estimates for a linear elasticity problem with Robin boundary conditions

TL;DR

This paper develops a detailed a priori error analysis for a linear elasticity problem with Robin boundary conditions, utilizing high-order curved meshes to improve discretization accuracy and validate results through numerical experiments in 2D and 3D.

Contribution

It introduces a novel error analysis framework for elasticity problems using curved meshes and the vector lift operator, providing new theoretical error estimates.

Findings

Error estimates depend on finite element degree and mesh order.

Numerical experiments confirm theoretical error bounds in 2D and 3D.

Curved meshes enhance the accuracy of elasticity problem discretization.

Abstract

This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the physical domain. The primary objective is to conduct a detailed error analysis for the elasticity problem using the vector lift operator, which maps vector-valued functions from the mesh domain to the physical domain. Error estimates are established, both in terms of the finite element approximation error and the geometric error, respectively associated to the finite element degree and to the mesh order. These theoretical a priori error estimates are validated by numerical experiments in 2D and 3D.