2014/08/01 by Ulrich Langer, Langer, Ulrich, Ioannis Toulopoulos +1 · 1 citation
Engineering · #65N12 #65N15 #65N35 #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.1408.0182
openalex publication_date 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study the approximation properties of multi-patch dG-IgA\nmethods, that apply the multipatch Isogeometric Analysis (IgA) discretization\nconcept and the discontinuous Galerkin (dG) technique on the interfaces between\nthe patches, for solving linear diffusion problems with diffusion coefficients\nthat may be discontinuous across the patch interfaces. The computational domain\nis divided into non-overlapping sub-domains, called patches in IgA, where\nB-splines, or NURBS finite dimensional approximations spaces are constructed.\nThe solution of the problem is approximated in every sub-domain without\nimposing any matching grid conditions and without any continuity requirements\nfor the discrete solution across the interfaces. Numerical fluxes with interior\npenalty jump terms are applied in order to treat the discontinuities of the\ndiscrete solution on the interfaces. We provide a rigorous a priori\ndiscretization error analysis for problems set in 2d- and 3d- dimensional\ndomains, with solutions belonging to Wl,p, l\≥ 2, p\∈\n(2d/(d+2(l-1)),2]. In any case, we show optimal convergence rates of the\ndiscretization with respect to the dG - norm.\n