Computing and Visualization in Science

, Volume 17, Issue 5, pp 217–233 | Cite as

Analysis of multipatch discontinuous Galerkin IgA approximations to elliptic boundary value problems

  • Ulrich Langer
  • Ioannis Toulopoulos


In this work, we study the approximation properties of multipatch dG-IgA methods, that apply the multipatch Isogeometric Analysis discretization concept and the discontinuous Galerkin technique on the interfaces between the patches, for solving linear diffusion problems with diffusion coefficients that may be discontinuous across the patch interfaces. The computational domain is divided into non-overlapping subdomains, called patches in IgA, where B-splines, or NURBS approximations spaces are constructed. The solution of the problem is approximated in every subdomain without imposing any matching grid conditions and without any continuity requirements for the discrete solution across the interfaces. Numerical fluxes with interior penalty jump terms are applied in order to treat the discontinuities of the discrete solution on the interfaces. We provide a rigorous a priori discretization error analysis for diffusion problems in two- and three-dimensional domains, where solutions patchwise belong to \(W^{l,p}\), with some \(l\ge 2\) and \( p\in ({2d}/{(d+2(l-1))},2]\). In any case, we show optimal convergence rates of the discretization with respect to the dG - norm.


Linear elliptic problems Discontinuous coefficients Discontinuous Galerkin discretization Isogeometric analysis Non-matching meshes Low regularity solutions A priori discretization error estimates 

Mathematics Subject Classification

65N12 65N15 65N35 



The authors thank A. Mantzaflaris, S. Moore and C. Hofer for their help on performing the numerical tests. This work was supported by Austrian Science Fund (FWF) under the grant NFN S117-03.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM) LinzAustria

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