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Quadrature for hp-Galerkin BEM in lR3


Sauter, S; Schwab, C (1997). Quadrature for hp-Galerkin BEM in lR3. Numerische Mathematik, 78(2):211-258.

Abstract

The Galerkin discretization of a Fredholm integral equation of the second kind on a closed, piecewise analytic surface is analyzed. High order, -boundary elements on grids which are geometrically graded toward the edges and vertices of the surface give exponential convergence, similar to what is known in the -Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete scheme preserving the exponential convergence of the -Boundary Element Method. The total work necessary for the consistent quadratures is shown to grow algebraically with the number of degrees of freedom. Numerical results on a curved polyhedron show exponential convergence with respect to the number of degrees of freedom as well as with respect to the CPU-time.

Abstract

The Galerkin discretization of a Fredholm integral equation of the second kind on a closed, piecewise analytic surface is analyzed. High order, -boundary elements on grids which are geometrically graded toward the edges and vertices of the surface give exponential convergence, similar to what is known in the -Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete scheme preserving the exponential convergence of the -Boundary Element Method. The total work necessary for the consistent quadratures is shown to grow algebraically with the number of degrees of freedom. Numerical results on a curved polyhedron show exponential convergence with respect to the number of degrees of freedom as well as with respect to the CPU-time.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:emhp/em Finite Element, Boundary Element Method, Numerical Integration, exponential convergence
Language:English
Date:1997
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:26
Publisher:Springer
ISSN:0029-599X
Publisher DOI:https://doi.org/10.1007/s002110050311
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0901.65069

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