# Finite Element Error Estimates on Geometrically Perturbed Domains

## TL;DR

This paper derives error estimates for finite element methods applied to elliptic PDEs on domains with geometric perturbations, highlighting the impact of domain mismatch on overall accuracy.

## Contribution

It provides new $H^1$ and $L_2$ error estimates for the Laplace problem on perturbed domains, emphasizing the significance of domain errors.

## Key findings

- Domain mismatch can dominate finite element errors.
- Error estimates are validated through computational examples.

## Abstract

We develop error estimates for the finite element approximation of elliptic partial differential equations on perturbed domains, i.e. when the computational domain does not match the real geometry. The result shows that the error related to the domain can be a dominating factor in the finite element discretization error. The main result consists of $H^1-$ and $L_2-$ error estimates for the Laplace problem. Theoretical considerations are validated by a computational example.