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

Author:
Harry Yserentant

Journal:
Math. Comp. **47** (1986), 399-409

MSC:
Primary 65N20; Secondary 65F10, 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856693-9

MathSciNet review:
856693

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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 -regular problems.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0856693-9

Article copyright:
© Copyright 1986
American Mathematical Society