118 citations · 565 across the 34 of their papers we have counts for
4 papers · 1 filter
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…
Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
Dmitri Kuzmin, Mária Lukácova-Medvid'ová, Philipp Öffner
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on…
Summation-by-parts operators for general function spaces: The second derivative
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developin…
Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recen…