Title

Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities

Document Type

Article

Publication Date

1-1-1999

Abstract

We consider the Poisson equation -Δu = f with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain Ω with re-entrant angles. A multigrid method for the computation of singular solutions and stress intensity factors using piecewise linear functions is analyzed. When f ∈ L (Ω), the rate of convergence to the singular solution in the energy norm is shown to be Script O sign(h), and the rate of convergence to the stress intensity factors is shown to be Script O sign(h , where w is the largest re-entrant angle of the domain and ∈ > 0 can be arbitrarily small. The cost of the algorithm is Script O sign(h ). When f ∈ H (Ω), the algorithm can be modified so that the convergence rate to the stress intensity factors is Script O sign(h ). In this case the maximum error of the multigrid solution over the vertices of the triangulation is shown to be Script O sign(h ). 2 1+(π/w)-∈) -2 1 2-∈ 2-∈

Publication Source (Journal or Book title)

Mathematics of Computation

First Page

559

Last Page

583

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