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Adaptive isogeometric boundary element methods with local smoothness control

Gregor Gantner

Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 107, 1090 GE Amsterdam, Netherlands

E-mail Address: [email protected]

Corresponding author.

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Dirk Praetorius

Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria

E-mail Address: [email protected]

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, and

Stefan Schimanko

Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria

E-mail Address: [email protected]

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https://doi.org/10.1142/S0218202520500074Cited by:6

Abstract

In the frame of isogeometric analysis, we consider a Galerkin boundary element discretization of the hyper-singular integral equation associated with the 2D Laplacian. We propose and analyze an adaptive algorithm which locally refines the boundary partition and, moreover, steers the smoothness of the NURBS ansatz functions across elements. In particular and unlike prior work, the algorithm can increase and decrease the local smoothness properties and hence exploits the full potential of isogeometric analysis. We prove that the new adaptive strategy leads to linear convergence with optimal algebraic rates. Numerical experiments confirm the theoretical results. A short appendix comments on analogous results for the weakly-singular integral equation.

Communicated by F. Brezzi

Keywords:

AMSC: 65D07, 65N38, 65N50, 65Y20

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Vol. 30, No. 02

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History

Received 5 March 2019

Revised 21 October 2019

Accepted 29 October 2019

Published: 5 February 2020

Keywords

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Adaptive isogeometric boundary element methods with local smoothness control

Abstract

References

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