The convergence of multilevel methods for solving finite-element equations in the presence of singularities

Yserentant, Harry

doi:10.1090/S0025-5718-1986-0856693-9

The convergence of multilevel methods for solving finite-element equations in the presence of singularities
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Math. Comp. 47 (1986), 399-409 Request permission

Abstract:

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 ${H^2}$-regular problems.

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