Geodesic
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 153-176.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 65N30, 65N15, 65N38
Keywords: boundary element method, hyper-singular integral equation, a posteriori error estimate, adaptive algorithm, convergence, optimality 
@article{ETNA_2015__44__a22,
     author = {Feischl, Michael and F\"uhrer, Thomas and Karkulik, Michael and Melenk, J.Markus and Praetorius, Dirk},
     title = {Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. {II:} {Hyper-singular} integral equation},
     journal = {Electronic transactions on numerical analysis},
     pages = {153--176},
     publisher = {mathdoc},
     volume = {44},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a22/}
}
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%A Karkulik, Michael
%A Melenk, J.Markus
%A Praetorius, Dirk
%T Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation
%J Electronic transactions on numerical analysis
%D 2015
%P 153-176
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Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J.Markus; Praetorius, Dirk. Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 153-176. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a22/