Discontinuous Galerkin Isogeometric Analysis for Elliptic Problems with Discontinuous Coefficients on Surfaces
For researchers in computational mechanics and isogeometric analysis, this work provides theoretical guarantees for handling complex industrial geometries with non-conforming patches and material discontinuities.
This paper extends a priori error estimates for discontinuous Galerkin isogeometric analysis to elliptic problems on surfaces with non-matching meshes and discontinuous diffusion coefficients across patch interfaces, and confirms the theory with numerical experiments.
This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $Ω\subset \mathbb{R}^3$. 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.