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.

Full Text (PDF) [1.4 MB], BibTeX

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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