Adaptive 2D IGA boundary element methods. (January 2016)

• Record Type: Journal Article
• Authors: Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
• Is Part Of: Engineering analysis with boundary elements. Volume 62(2016:Jan.)
• Page Start: 141
• Page End: 153
• Publication Date: 2016-01
• Subjects: Isogeometric analysis -- Boundary element method -- Collocation -- A posteriori error estimate -- Adaptive mesh-refinement; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2015.10.003
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error estimator for Galerkin IGA boundary element methods, the present work focuses more on collocation and weighted-residual error estimators, which provide reliable upper bounds for the energy error. Our analysis allows piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. We formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments show that the proposed adaptive strategy leads to optimal convergence, and related IGA boundary element methods are superior to standard boundary element methods with piecewise polynomials.