Discontinuous Galerkin Isogeometric Analysis for Elliptic Problems with Discontinuous Coefficients on Surfaces

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\mathrm{\Omega }\subset {\mathbb{R}}^3$. 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 $\mathit{\text{a}}\mathit{\text{priori}}$ 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 $\mathit{\text{a}}\mathit{\text{priori}}$ error estimate for the symmetric discontinuous Galerkin scheme and numerical experiments to confirm the theory.