3 papers
math.NA2026
Volume Term Adaptivity for Discontinuous Galerkin Schemes
Daniel Doehring, Jesse Chan, Hendrik Ranocha +3
We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we…
math.NA2025
Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration
Daniel Doehring, Hendrik Ranocha, Manuel Torrilhon
We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws an…
math.NA2024
Fourth-Order Paired-Explicit Runge-Kutta Methods
Daniel Doehring, Lars Christmann, Michael Schlottke-Lakemper +2
In this paper, we extend the Paired-Explicit Runge-Kutta schemes by Vermeire et. al. to fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta metho…