Uniform Convergence of the Multigrid V -cycle on Graded Meshes
نویسندگان
چکیده
We prove the uniform convergence of the multigrid V -cycle on graded meshes for corner-like singularities of elliptic equations on a bounded domain Ω ⊂ IR. In particular, using some weighted Sobolev space K a (Ω) and the method of subspace corrections with the elliptic projection decomposition estimate on K a (Ω), we show that the multigrid V -cycle converges uniformly for piecewise linear functions with standard smoothers (Richardson, weighted Jacobi, Gauss-Seidel, etc.).
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