Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated

Abstract: We study two techniques for correcting the geometrical error associated with domain approximation by a polygon. The first was introduced some time ago \cite{bramble1972projection} and leads to a nonsymmetric formulation for Poisson's equation. We introduce a new technique that yields a symmetric formulation and has similar performance. We compare both methods on a simple test problem.