2015/11/18 by Christoph K. Hofer, Ulrich Langer, Hofer, Christoph +3
Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1511.05715
openalex publication_date 2015/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique\nfor the numerical solution of elliptic diffusion problems in computational\ndomains decomposed into volumetric patches with non-matching interfaces. Due to\nan incorrect segmentation procedure, it may happen that the interfaces of\nadjacent subdomains don't coincide. In this way, gap regions, which are not\npresent in the original physical domain, are created. In this paper, the gap\nregion is considered as a subdomain of the decomposition of the computational\ndomain and the gap boundary is taken as an interface between the gap and the\nsubdomains. We apply a multi-patch approach and derive a subdomain variational\nformulation which includes interface continuity conditions and is consistent\nwith the original variational formulation of the problem. The last formulation\nis further modified by deriving interface conditions without the presence of\nthe solution in the gap. Finally, the solution of this modified problem is\napproximated by a special discontinuous Galerkin IgA technique. The ideas are\nillustrated on a model diffusion problem with discontinuous diffusion\ncoefficients. We develop a rigorous theoretical framework for the proposed\nmethod clarifying the influence of the gap size onto the convergence rate of\nthe method. The theoretical estimates are supported by numerical examples in\ntwo- and three-dimensional computational domains.\n