Finite Element Error Estimates on Geometrically Perturbed Domains

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.