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Multipatch discontinuous Galerkin isogeometric analysis. (English) Zbl 1334.65194
Jüttler, Bert (ed.) et al., Isogeometric analysis and applications 2014. Selected papers based on the presentations at the IGAA 2014, Annweiler am Trifels, Germany, April 7–10, 2014. Cham: Springer (ISBN 978-3-319-23314-7/hbk; 978-3-319-23315-4/ebook). Lecture Notes in Computational Science and Engineering 107, 1-32 (2015).
Summary: Isogeometric Analysis (IgA) uses the same class of basis functions for both representing the geometry of the computational domain and approximating the solution of the boundary value problem under consideration. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping subdomains also called patches in the geometrical framework. We will present discontinuous Galerkin (dG) methods that allow for discontinuities across the subdomain (patch) boundaries. The required interface conditions are weakly imposed by the dG terms associated with the boundary of the subdomains. The construction and the corresponding discretization error analysis of such dG multi-patch IgA schemes is given for heterogeneous diffusion model problems in volumetric 2d and 3d domains as well as on open and closed surfaces. The theoretical results are confirmed by numerous numerical experiments which have been performed in G+SMO. The concept and the main features of the IgA library G+SMO are also described.
For the entire collection see [Zbl 1337.65003].

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
Software:
Eigen
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