The convergence of multilevel methods for solving finite-element equations in the presence of singularities
Harry Yserentant · Mathematics of Computation · 1986
The known convergence proofs for multi-level methods assume the quasi-uniformity of the family of domain triangulations used. Such triangulations are not suitable for problems with singularities caused by re-entrant corners and abrupt changes in the boundary conditions. In this paper it is shown that families of properly refined grids yield the same convergence behavior of multi-level methods for such singular problems as quasi-uniform subdivisions do for H 2 {H^2} -regular problems.