Penalty combinations of the Ritz-Calerkin and finite difference methods for singularity problems

[摘要] Penalty combination of the Ritz-Galerkin and finite difference methods is presented for solving elliptic boundary value problems with singularities. The superconvergence rate, O(h(2-delta)), Of solution derivatives by the combination can be achieved while using quasiuniform rectangular difference grids, where h is the maximal mesh length of difference grids used in the finite difference method, and delta(> 0) is an arbitrarily small number. It is due to its simplicity that the penalty combination of the Ritz-Galerkin and finite difference methods is highly recommended for solving the complicated problems with multiple singularities and multiple interfaces.

[发布日期] 1997-06-01

[关键词] superconvergence;combined method;coupling strategy;finite elliptic equation;singularity problem;superconvergence;combined method;coupling strategy;finite difference method;Ritz-Galerkin method;penalty method