Volume 44, pp. 153-176, 2015.

Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. Part II: hyper-singular integral equation

Michael Feischl, Thomas Führer, Michael Karkulik, J. Markus Melenk, and Dirk Praetorius

Abstract

We analyze an adaptive boundary element method with fixed-order piecewise polynomials for the hyper-singular integral equation of the Laplace-Neumann problem in 2D and 3D which incorporates the approximation of the given Neumann data into the overall adaptive scheme. The adaptivity is driven by some residual-error estimator plus data oscillation terms. We prove convergence with quasi-optimal rates. Numerical experiments underline the theoretical results.

Full Text (PDF) [476 KB]

Key words

boundary element method, hyper-singular integral equation, a posteriori error estimate, adaptive algorithm, convergence, optimality

AMS subject classifications

65N30, 65N15, 65N38

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