Discontinuous galerkin isogeometric analysis for elliptic problems with discontinuous diffusion coefficients on surfaces

Abstract

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dG-IGA) as a numerical treatment of Difusion problems on orientable surfaces Ω ⊂ R 3. The computational domain or surface considered consist of several non-overlapping sub-domains or patches which are coupled via an interior penalty scheme. In Langer and Moore [13], we presented a priori error estimate for conforming computational domains with matching meshes across patch interface and a constant difusion coefcient. However, in this article, we generalize the a priori error estimate to non-matching meshes and discontinuous difusion coefcients 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 confrm the theory