Space-Time Multi-patch Discontinuous Galerkin Isogeometric Analysis for Parabolic Evolution Problems

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 moving space-time computational domains. Following \cite{LangerMooreNeumueller:2016a}, 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 $\mathit{\text{a}}\mathit{\text{priori}}\mathit{\text{discretization}}$ 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.