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
Recommended Citation
Brenner, S., & Sung, L. (1997). Multigrid methods for the computation of singular solutions and stress intensity factors II: Crack singularities. BIT Numerical Mathematics, 37 (3), 623-643. https://doi.org/10.1007/BF02510243
