Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results

In [Z. Cai and S. Kim, SIAM J. Numer. Anal., 39 (2001), pp. 286--299], we developed a new finite element method using singular functions for the Poisson equation on a polygonal domain with re-entrant angles. Such a method first computes the regular part of the solution, then the stress intensity factor, and finally the solution itself. This paper studies solution methods for solving the system of linear equations arising from the discretization and focuses on numerical results including the finite element accuracy and the multigrid performance.