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Register a new userA posteriori error analysis for a boundary element method with non-conforming domain decomposition
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We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a non-conforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasi-reliability and efficiency of the error estimator in comparison with the error in a natural (non-conforming) norm. Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results.
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This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions which hold for a large class of discretizations. Efficiency of the error estimate is shown for a natural discretization of low order. Numerical examples confirm the theoretical results. The resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems.
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We present and analyze a non-conforming domain decomposition approximation for a hypersingular operator governed by the Helmholtz equation in three dimensions. This operator appears when considering the corresponding Neumann problem in unbounded domains exterior to open surfaces. We consider small wave numbers and low-order approximations with Nitsche coupling across interfaces. Under appropriate assumptions on mapping properties of the weakly singular and hypersingular operators with Helmholtz kernel, we prove that this method converges almost quasi-optimally. Numerical experiments confirm our error estimate.
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