Abstract

We present the first a priori error analysis of a technique that allows us to numerically solve steady-state diffusion problems defined on curved domains Omega by using finite element methods defined in polyhedral subdomains D-h subset of Omega. For a wide variety of hybridizable discontinuous Galerkin and mixed methods, we prove that the order of convergence in the L-2-norm of the approximate flux and scalar unknowns is optimal as long as the distance between the boundary of the original domain G and that of the computational domain Gamma(h) is of order h. We also prove that the L-2-norm of a projection of the error of the scalar variable superconverges with a full additional order when the distance between Gamma and Gamma(h) is of order h(5/4) but with only half an additional order when such a distance is of order h. Finally, we present numerical experiments confirming the theoretical results and showing that even when the distance between Gamma and Gamma(h) is of order h, the above-mentioned projection of the error of the scalar variable can still superconverge with a full additional order.