2 papers
math.NA2025
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…
math.NA2024
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…