Space-time multi-patch discontinuous galerkin isogeometric analysis for parabolic evolution problems

Abstract

We present and analyze a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic evolution equations in deforming space-time computational domains. Following [20], we use a time-upwind test function and apply multi-patch discontinuous Galerkin IgA methodology for discretizing the evolution problem both in space and in time. This yields a discrete bilinear form which is elliptic on the IgA space with respect to a space-time dG norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the space-time dG norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces