Space-Time Multi-patch Discontinuous Galerkin Isogeometric Analysis for Parabolic Evolution Problems
This work provides a theoretical foundation and numerical validation for a space-time dG-IgA method, which is relevant for computational scientists solving parabolic problems on complex moving domains.
The authors present a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for parabolic evolution equations in moving domains, proving a priori error estimates and confirming them with numerical experiments.
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 \textit{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.