Structure aware Runge-Kutta time stepping for spacetime tents

Abstract

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