document: Isogeometric analysis. The central idea of isogeometric analysis is to use the same ansatz functions for the discretization of the partial differential equation at hand, as are used for the representation of the problem geometry. Usually, the problem geometry Ω is represented in computer aided design (CAD) by means of NURBS or T-splines. This concept, originally invented in [1] for finite element methods (IGAFEM) has proved very fruitful in applications [1,2]; see also the monograph [3]. Since CAD directly provides a parametrization of the boundary ∂Ω, this makes the boundary element method (BEM) the most attractive numerical scheme, if applicable (i.e., provided that the fundamental solution of the differential operator is explicitly known). Isogeometric BEM (IGABEM) has first been considered for 2D BEM in [4] and for 3D BEM in [5]. Unlike standard BEM with piecewise polynomials which is well-studied in the literature, cf. the monographs [6,7] and the references therein, the numerical analysis of IGABEM is essentially open. We only refer to [2,8–10] for numerical experiments and to [11] for some quadrature analysis. In particular, a posteriori error estimation has been well-studied for standard BEM, e.g., [12–18] as well as the recent overview article [19], but has not been treated for IGABEM so far. The purpose of the present work is to shed some first light on a posteriori error analysis for IGABEM which provides some mathematical foundation of a corresponding adaptive algorithm.
doc_bio_tags: B I O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O B I O O B I O O O O B I I B O O O B O O O O O O O O O B I I B O O O O O O O O O O O O O B O O O O O O O O O O O B I I B O O O B I O O O O O O O O O O O O O O O O B B O O O O O B I O O O O B I O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B I O O B I I I O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B I I I O B O O O O O O O O B I
extractive_keyphrases: 2d bem 3d bem adaptive algorithm ansatz functions a posteriori error analysis a posteriori error estimation bem boundary element method cad computer aided design finite element methods igabem igafem isogeometric analysis numerical scheme nurbs problem geometry quadrature analysis
abstractive_keyphrases: isogeometric bem mathematical foundation of a corresponding adaptive algorithm numerical analysis of igabem shed some first light on a posteriori error analysis for igabem standard bem t-splines