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 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 Langer and Moore [13], 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.