Discontinuous Galerkin isogeometric analysis for elliptic problems with discontinuous diffusion coefficients on surfaces. (English) Zbl 1450.65148
Summary: This paper is concerned with using discontinuous Galerkin isogeometric analysis (dG-IGA) as a numerical treatment of diffusion problems on orientable surfaces \(\Omega \subset \mathbb{R}^3\). The computational domain or surface considered consists of several non-overlapping subdomains or patches which are coupled via an interior penalty scheme. In [U. Langer and the author, Lect. Notes Comput. Sci. Eng. 104, 319–326 (2016; Zbl 1339.65219)], we presented a priori error estimate for conforming computational domains with matching meshes across patch interface and a constant diffusion coefficient. However, in this article, we generalize the a priori error estimate to non-matching meshes and discontinuous diffusion coefficients across patch interfaces commonly occurring in industry. We construct B-spline or NURBS approximation spaces which are discontinuous across patch interfaces. We present a priori error estimate for the symmetric discontinuous Galerkin scheme and numerical experiments to confirm the theory.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 74S22 | Isogeometric methods applied to problems in solid mechanics |
Keywords:
discontinuous Galerkin; multi-patch isogeometric analysis; elliptic problems; a priori error analysis; surface PDE; interior penalty Galerkin; Laplace-Beltrami; discontinuous coefficientsCitations:
Zbl 1339.65219Software:
G+SmoReferences:
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