Adaptive meshless Galerkin boundary node methods for hypersingular integral equations |
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Authors: | Xiaolin Li |
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Institution: | College of Mathematics Science, Chongqing Normal University, Chongqing 400047, PR China |
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Abstract: | Adaptive refinement techniques are developed in this paper for the meshless Galerkin boundary node method for hypersingular boundary integral equations. Two types of error estimators are derived. One is a perturbation error estimator that is formulated based on the difference between numerical solutions obtained using two consecutive nodal arrangements. The other is a projection error estimator that is formulated based on the difference between the numerical solution itself and its projection. These error estimators are proven to have an upper and a lower bound by the constant multiples of the exact error in the energy norm. A localization scheme is presented to accomodate the non-local property of hypersingular integral operators for the needed computable local error indicators. The convergence of the adaptive meshless techniques is verified theoretically. To confirm the theoretical results and to show the efficiency of the adaptive techniques, numerical examples in 2D and 3D with high singularities are provided. |
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Keywords: | Meshless method Adaptive analysis A posteriori error estimate Galerkin boundary node method Hypersingular boundary integral equations Convergence |
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