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Local convergence of the boundary element method on polyhedral domains. (English) Zbl 1402.65173

Summary: The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm’s integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a priori estimates in \(L^2\) for Symm’s integral equation and in \(H^1\) for the hyper-singular equation. The local rate of convergence is limited by the local regularity of the sought solution and the sum of the rates given by the global regularity and additional regularity provided by the shift theorem for a dual problem.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations

Software:

HILBERT
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Full Text: DOI arXiv

References:

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