ADAPTED NUMERICAL METHODS FOR THE POISSON EQUATION WITH L-2 BOUNDARY DATA IN NONCONVEX DOMAINS

摘要

The very weak solution of the Poisson equation with L-2 boundary data is de fined by the method of transposition. The finite element solution with regularized boundary data converges in the L-2 (Omega)-norm with order 1/2 in convex domains but has a reduced convergence order in nonconvex domains although the solution remains to be contained in H-1/2 ( Omega). The reason is a singularity in the dual problem. In this paper we propose and analyze, as a remedy, both a standard fi nite element method with mesh grading and a dual variant of the singular complement method. The error order 1/2 is retained in both cases, also with nonconvex domains. Numerical experiments con fi rm the theoretical results.