Entropy production by implicit Runge-Kutta schemes

Abstract

This paper follows up on the author's recent paper "Entropy Production by Explicit Runge-Kutta schemes", where a formula for the production of entropy by fully discrete schemes with explicit Runge-Kutta time integrators was presented. In this paper, the focus is on implicit Runge-Kutta schemes, for which the fully discrete numerical entropy evolution scheme is derived and tested.

arXiv commentThis is a postprint (accepted version) of an article published in the Journal of Scientific Computing. The published version may differ from this postprint and is available at: Lozano, C J Sci Comput (2019) https://doi.org/10.1007/s10915-019-00914-5

References in corpus (1)

• On entropy stable temporal fluxes

Cited by in corpus (4)

• General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
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• Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
• Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations