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
Recommended Citation
Brenner, S. (1999). Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities. Mathematics of Computation, 68 (226), 559-583. https://doi.org/10.1090/s0025-5718-99-01017-0
