For the Poisson equation - δ u = f ( x , y ) on an L-shaped region in the plane with zero boundary conditions, the author establishes superconvergence rates of the solution gradients on the entire domain for a combination of a Ritz-Galerkin method and a finite element method. The domain is subdivided into two disjoint subdomains S1 and S2 , where ∂ S2 includes the boundary singularity. On S1 , bilinear elements are used, while singular functions are chosen on S2. Li shows that this hybrid combination provides a global rate of O ( h2 ) in the Sobolev norm ∥ &dundot; ∥ 1 over the subdomains S1 and S2, where h is the maximal grid size of the mesh on S1. Some numerical examples confirm this rate.
