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
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},
     year = {2015},
     volume = {44},
     zbl = {1312.65173},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a22/}
}
TY  - JOUR
AU  - Feischl,  Michael
AU  - Führer,  Thomas
AU  - Karkulik,  Michael
AU  - Melenk,  J.Markus
AU  - Praetorius,  Dirk
TI  - Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation
JO  - Electronic transactions on numerical analysis
PY  - 2015
SP  - 153
EP  - 176
VL  - 44
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__44__a22/
LA  - en
ID  - ETNA_2015__44__a22
ER  - 
%0 Journal Article
%A Feischl,  Michael
%A Führer,  Thomas
%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
%V 44
%U http://geodesic.mathdoc.fr/item/ETNA_2015__44__a22/
%G en
%F ETNA_2015__44__a22
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/