Volume 49, pp. 126-150, 2018.

Time-multipatch discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems

Christoph Hofer, Ulrich Langer, Martin Neumüller, and Ioannis Toulopoulos

Abstract

In this paper, we present a new time-multipatch discontinuous Galerkin Isogeometric Analysis (IgA) technology for solving parabolic initial-boundary problems in space and time simultaneously. We prove coercivity of the IgA variational problem with respect to a suitably chosen norm that together with boundedness, consistency, and approximation results yields a priori discretization error estimates in this norm. Furthermore, we provide efficient parallel generation and parallel multigrid solution technologies. Finally, we present first numerical results on massively parallel computers.

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Key words

parabolic initial-boundary value problems, space-time isogeometric analysis, time discontinuous Galerkin methods, space-time multigrid solvers

AMS subject classifications

35K20, 65M12, 65M15, 65M55

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