Adaptive-Additive Multilevel Methods for Hypersingular Integral Equation |
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Authors: | Thang Cao |
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Institution: | School of Mathematics , University of New South Wales , Sydney, NSW, 2052, Australia |
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Abstract: | In this article we present the combined adaptive-additive multilevel methods for the Galerkin approximation of hypersingular integral equation on the interval o = ( m 1,1). We also derive an efficient and reliable a posteriori error estimate for the error between the exact solution u and the approximated multilevel solution $ \tilde u_ {\cal M} $ , measuring locally the quality of $ \tilde u_ {\cal M} $ . The algorithm is carefully designed to obtain minimal complexity. A limitation of our analysis approach is that the meshes must be assumed to be quasi-uniform. |
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Keywords: | Adaptive-additive Multilevel Method Galerkin Approximation A Posteriori Estimates Hypersingular Integral Equations |
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