Adaptive isogeometric boundary element methods with local smoothness control

Author:

Gantner Gregor1,Praetorius Dirk2,Schimanko Stefan2

Affiliation:

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

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

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.

Funder

Optimal isogeometric boundary element method

Optimal adaptivity for BEM and FEM-BEM coupling

Dissipation and dispersion in nonlinear PDEs

Taming complexity in PDE systems

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

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