t is well known that Galerkin discretizations based on hp-finite element spaces are converging exponentially with respect to the degrees of freedom for elliptic problems with piecewise analytic data. However, the question whether these methods can be realized for general situations such that the exponential convergence is preserved also with respect to the computing time is very essential.

We show how the numerical quadrature can be realized in order that the resulting fully discrete hp-boundary element method (BEM) converges exponentially with algebraically growing work. The key point is to approximate the integrals constituting the stiffness matrix by exponentially converging cubature methods.

Sauter, S; Schwab, C (1996). *Realization of hp-Galerkin BEM in R³.* In: Hackbusch, W; Wittum, G. Boundary elements: implementation and analysis of advanced algorithms (Kiel, 1996). Braunschweig: Vieweg, 194-206.

## Abstract

t is well known that Galerkin discretizations based on hp-finite element spaces are converging exponentially with respect to the degrees of freedom for elliptic problems with piecewise analytic data. However, the question whether these methods can be realized for general situations such that the exponential convergence is preserved also with respect to the computing time is very essential.

We show how the numerical quadrature can be realized in order that the resulting fully discrete hp-boundary element method (BEM) converges exponentially with algebraically growing work. The key point is to approximate the integrals constituting the stiffness matrix by exponentially converging cubature methods.

## Citations

## Additional indexing

Other titles: | Proceedings of the 12th GAMM-Seminar held at the Christian-Albrechts-University, Kiel, January 19–21, 1996 |
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Item Type: | Book Section, refereed, original work |

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 1996 |

Deposited On: | 29 Nov 2010 16:28 |

Last Modified: | 05 Apr 2016 13:27 |

Publisher: | Vieweg |

Series Name: | Notes on Numerical Fluid Mechanics |

Number: | 54 |

ISSN: | 0179-9614 |

ISBN: | 3-528-07654-2 |

Related URLs: | http://opac.nebis.ch/F/?local_base=EBI01&con_lng=GER&func=find-b&find_code=090&request=000602727 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0881.65115 |

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