This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{ R}^3$. 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 U. Langer and S. E. Moore,2014, 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 \textit{ 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 \textit{ a priori} error estimate for the symmetric discontinuous Galerkin scheme and numerical experiments to confirm the theory.
Categories: math.NA