Title

Multigrid methods for the computation of singular solutions and stress intensity factors II: Crack singularities

Document Type

Article

Publication Date

1-1-1997

Abstract

We consider the Poisson equation -Δu = f with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain Ω with cracks. Multigrid methods for the computation of singular solutions and stress intensity factors using piecewise linear functions are analyzed. The convergence rate for the stress intensity factors is O(h ) when f ∈ L (Ω) and O(h ) when f ∈ H (Ω). The convergence rate in the energy norm is O(h ) in the first case and O(h) in the second case. The costs of these multigrid methods are proportional to the number of elements in the triangulation. The general case where f ∈ H (Ω) is also discussed. (3/2)-∈ 2 2-∈ 1 1-∈ m

Publication Source (Journal or Book title)

BIT Numerical Mathematics

First Page

623

Last Page

643

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