Overcoming corner singularities using multigrid methods

This work was supported in part by National Science Foundation grants DMS-94-96275 and DMS-96-00133 We consider the Poisson equation -δu = f with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain ω. We develop a finite element multigrid method on quasi-uniform grids that obtains O (h ) convergence in the H (ω) norm for any positive ε when f ∈ H (ω). The cost of the method is proportional to the number of elements in the triangulation. The results of this paper can be generalized to other equations and other boundary conditions. m+1-ε 1