  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.
