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Mathematics of Computation

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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 $ {H^2}$-regular problems.


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DOI: https://doi.org/10.1090/S0025-5718-1986-0856693-9
Article copyright: © Copyright 1986 American Mathematical Society