Full numerical quadrature of weakly singular double surface integrals in Galerkin boundary element methods

2011 ◽  
Vol 27 (2) ◽  
pp. 314-334 ◽  
Author(s):  
J. D'Elía ◽  
L. Battaglia ◽  
A. Cardona ◽  
M. Storti
Keyword(s):  
Boundary Element ◽  
Boundary Element Methods ◽  
Numerical Quadrature ◽  
Weakly Singular ◽  
Double Surface ◽  
Galerkin Boundary Element Methods ◽  
Surface Integrals

scholarly journals Adaptive boundary-element methods for transmission problems

1997 ◽  
Vol 38 (3) ◽  
pp. 336-367 ◽  
Author(s):  
Carsten Carstensen ◽  
Ernst P. Stephan
Keyword(s):  
Boundary Element ◽  
Boundary Integral Equations ◽  
Integral Operators ◽  
Adaptive Algorithms ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
A Posteriori ◽  
Multiplicative Constant ◽  
Transmission Problems ◽  
Weakly Singular

AbstractIn this paper we present an adaptive boundary-element method for a transmission prob-lem for the Laplacian in a two-dimensional Lipschitz domain. We are concerned with an equivalent system of boundary-integral equations of the first kind (on the transmission boundary) involving weakly-singular, singular and hypersingular integral operators. For the h-version boundary-element (Galerkin) discretization we derive an a posteriori error estimate which guarantees a given bound for the error in the energy norm (up to a multiplicative constant). Then, following Eriksson and Johnson this yields an adaptive algorithm steering the mesh refinement. Numerical examples confirm that our adaptive algorithms yield automatically good triangulations and are efficient.

scholarly journals Adaptive Galerkin boundary element methods with panel clustering

2006 ◽  
Vol 105 (4) ◽  
pp. 603-631 ◽  
Author(s):  
Wolfgang Hackbusch ◽  
Boris N. Khoromskij ◽  
Stefan Sauter
Keyword(s):  
Boundary Element ◽  
Boundary Element Methods ◽  
Galerkin Boundary Element Methods
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