Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions. Issue 13 (3rd October 2021)

• Record Type: Journal Article
• Authors: Hofer, Christoph; Toulopoulos, Ioannis
• Is Part Of: Applicable analysis. Volume 100:Issue 13(2021)
• Page Start: 2749
• Page End: 2776
• Publication Date: 2021-10-03
• Subjects: Elliptic diffusion problems -- heterogeneous diffusion coefficients -- isogeometric analysis -- non-matching parametrized interfaces -- overlapping patches -- discontinuous Galerkin methods -- consistency error; 65M12 -- 65M15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1698724
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g. provided by a Computer Aided Design model. Typically, small gaps and overlapping regions can appear at the patch interfaces of such multipatch representations. In the current work, we consider multipatch representations having only small overlapping regions between the patches. We develop a Discontinuous Galerkin (DG)-IGA method that can be immediately applied to these representations. Our method appropriately connects the fluxes of the one face of the overlapping region with the flux of the opposite face. We provide a theoretical justification of our approach by splitting the whole error into two components: the first is related to the incorrect representation of the patches (consistency error) and the second to the approximation properties of the IGA space. We show bounds for both components of the error. We verify the theoretical error estimates in a series of numerical examples.