[HTML][HTML] On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws

H Ranocha, AR Winters, M Schlottke-Lakemper… - Journal of …, 2025 - Elsevier
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 …

Local subcell monolithic DG/FV convex property preserving scheme on unstructured grids and entropy consideration

F Vilar - Journal of Computational Physics, 2025 - Elsevier
This article aims at presenting a new local subcell monolithic Discontinuous-Galerkin/Finite-
Volume (DG/FV) convex property preserving scheme solving system of conservation laws on …

[LIBRO][B] Property-preserving numerical schemes for conservation laws

D Kuzmin, H Hajduk - 2024 - World Scientific
Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

[HTML][HTML] A flux-differencing formula for split-form summation by parts discretizations of non-conservative systems: applications to subcell limiting for magneto …

AM Rueda-Ramírez, GJ Gassner - Journal of Computational Physics, 2024 - Elsevier
In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of
general non-conservative systems of hyperbolic balance laws can be rewritten as a finite …

[HTML][HTML] Monolithic convex limiting and implicit pseudo-time step** for calculating steady-state solutions of the Euler equations

P Moujaes, D Kuzmin - Journal of Computational Physics, 2025 - Elsevier
In this work, we use the monolithic convex limiting (MCL) methodology to enforce relevant
inequality constraints in implicit finite element discretizations of the compressible Euler …

High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting

Y Lin, J Chan - Journal of Computational Physics, 2024 - Elsevier
Subcell limiting strategies for discontinuous Galerkin spectral element methods do not
provably satisfy a semi-discrete cell entropy inequality. In this work, we introduce an …

[HTML][HTML] A flux-differencing formulation with Gauss nodes

A Mateo-Gabín, AM Rueda-Ramírez, E Valero… - Journal of …, 2023 - Elsevier
In this work, we propose an extension of telescopic derivative operators for the DGSEM with
Gauss nodes, and we prove that this formulation is equivalent to its usual matrix counterpart …

On the conservation property of positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations

Z Xu, CW Shu - Journal of Computational Physics, 2023 - Elsevier
Recently, there has been a series of works on the positivity-preserving discontinuous
Galerkin methods for stationary hyperbolic equations, where the notion of mass …

Dissipative WENO stabilization of high-order discontinuous Galerkin methods for hyperbolic problems

J Vedral - arxiv preprint arxiv:2309.12019, 2023 - arxiv.org
We present a new approach to stabilizing high-order Runge-Kutta discontinuous Galerkin
(RKDG) schemes using weighted essentially non-oscillatory (WENO) reconstructions in the …