Structure aware Runge–Kutta time stepping for spacetime tents

Jay Gopalakrishnan (), Joachim Schöberl () and Christoph Wintersteiger ()
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Jay Gopalakrishnan: Portland State University
Joachim Schöberl: Technische Universität Wien
Christoph Wintersteiger: Technische Universität Wien

Partial Differential Equations and Applications, 2020, vol. 1, issue 4, 1-24

Abstract: Abstract We introduce a new class of Runge–Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge–Kutta methods, the new methods yield expected convergence properties when standard high order spatial (discontinuous Galerkin) discretizations are used. After presenting a derivation of nonstandard order conditions for these methods, we show numerical examples of nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We also report on the discrete stability properties of these methods applied to linear hyperbolic equations.

Keywords: Local time stepping; Spacetime; Causality; 65M60; 65M20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00020-4

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