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

Abstract

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion 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 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.

Multipatch Discontinuous Galerkin IGA for the Biharmonic Problem On Surfaces

“…Multipatch discontinuous Galerkin IGA has been introduced and analyzed for second order elliptic problems on surfaces with matching and non-matching meshes, see e.g. [12,11,20,17]. Here, the computational domain consists of several conforming non-overlapping subdomains.…”