The simplified hybrid-combined methods for Laplace's equation with singularities

摘要

In Li and Liang (1983), the simplified hybrid-combined method is presented for combining the Ritz-Galerkin method and the finite-element method. In this paper we will apply this method to solve singularity problems of Laplace's equation. Error bounds and stability analyses will be provided while taking into account the integration approximation along the coupling boundary. A significant coupling relation between the Ritz-Galerkin and the finite-element method has been found for the Laplace equation with singularities. An optimal rate of convergence has also been achieved. Numerical experiments have been carried out for solving the benchmark problem: Motz's problem to verify the theoretical results.