307 citations
- Auckland University of TechnologyNZ5 papers
- Leibniz University HannoverDE5 papers
- IT University of CopenhagenDK4 papers
- Karlsruhe Institute of TechnologyDE4 papers
- Reutlingen UniversityDE4 papers
- Technical University of MunichDE4 papers
- TU WienAT4 papers
- Centre National de la Recherche ScientifiqueFR3 papers
- The University of Texas at AustinUS3 papers
- University of TartuEE3 papers
- Aix-Marseille UniversitéFR2 papers
- Board of the Swiss Federal Institutes of TechnologyCH2 papers
5 papers · 1 filter
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Öffner +1
For hyperbolic conservation laws, the famous Lax-Wendroff theorem delivers sufficient conditions for the limit of a convergent numerical method to be a weak (entropy) solution. Thi…
Theoretical analysis of a finite-volume scheme for a stochastic Allen-Cahn problem with constraint
Caroline Bauzet, Cédric Sultan, Guy Vallet +1
The aim of this contribution is to address the convergence study of a time and space approximation scheme for an Allen-Cahn problem with constraint and perturbed by a multiplicativ…
Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods
Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters +3
High-order numerical methods for conservation laws are highly sought after due to their potential efficiency. However, it is challenging to ensure their robustness, particularly fo…
A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations
Mirco Ciallella, Lorenzo Micalizzi, Victor Michel-Dansac +2
In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inh…
On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper +3
We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this con…