On the boundary element method with mesh refinement on curves with corners

摘要

An indirect boundary integral formulation for the boundary value of the Laplacian will be given. This leads to the integral of the first kind. We study the problem on the boundary curve of some polygon. The Galerkin scheme for solving the boundary integral equation is analyzed.For the approximation of the solution we use B-spline spaces on graded meshes, which are adapted to the known singularity of the boundary charge at the edges. We derive optimal order global error estimates in various Sobolev norms for the Galerkin solution. The numerical analysis is based on the uniqueness of he solution, a coersiveness inequality and the regularity properties of the solution.