Adaptive isogeometric boundary element methods with local smoothness control

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.

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Cited by in corpus (5)

• Mathematical foundations of adaptive isogeometric analysis
• Adaptive IGAFEM with optimal convergence rates: T-splines
• Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
• Stable implementation of adaptive IGABEM in 2D in MATLAB
• Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations