The Fourier-finite element method for the Poisson problem on a non-convex polyhedral cylinder

Abstract

We study the Poisson problem with zero boundary datum in a (finite) polyhedral cylinder with a non-convex edge. Applying the Fourier sine series to the equation along the edge and by a corner singularity expansion for the Poisson problem with parameter, we define the edge flux coefficient and the regular part of the solution on the polyhedral cylinder. We present a numerical method for approximating the edge flux coefficient and the regular part and show the stability. We derive an error estimate and give some numerical experiments. (C) 2009 Elsevier B.V. All rights reserved.