Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 51, Issue 2, Pages 1327-1348Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110842569
Keywords
adaptive boundary element method; adaptive algorithm; error reduction; optimal convergence
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Funding
- FWF project Adaptive Boundary Element Method
- Austrian Science Fund (FWF) [P21732]
- Austrian Science Fund (FWF) [P21732] Funding Source: Austrian Science Fund (FWF)
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For the simple layer potential V associated with the three-dimensional (3D) Laplacian, we consider the weakly singular integral equation V phi = f. This equation is discretized by the lowest-order Galerkin boundary element method. We prove convergence of an h-adaptive algorithm that is driven by a weighted residual error estimator. Moreover, we identify the approximation class for which the adaptive algorithm converges quasi-optimally with respect to the number of elements. In particular, we prove that adaptive mesh refinement is superior to uniform mesh refinement.
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