The Convergence of Multi-Level Methods for Solving Finite-Element Equations in the Presence of Singularities

Harry Yserentant
1986 Mathematics of Computation  
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 r72-regular problems.
doi:10.2307/2008163 fatcat:k5n4zmp6jnh7bhmpwtahmmka4q