A multigrid method on graded meshes for a hypersingular integral equation
نویسنده
چکیده
We consider an integral equation obtained by the “direct method” for the Neumann problem on a polygonal domain which may contain slits, i.e., interior angles of 2π. By using a Galerkin method with piecewise linear functions on a suitable graded mesh one can obtain the optimal convergence rate h3/2. Using a Gauss solver for the arising linear system would require C h−3 operations. We show that a multigrid method can solve the linear system with an accuracy of the order of the Galerkin error with only C h−2 operations.
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