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The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that…

Numerical Analysis · Mathematics 2015-03-11 Michael Dumbser , Olindo Zanotti , Raphael Loubere , Steven Diot

We propose a new high order accurate nodal discontinuous Galerkin (DG) method for the solution of nonlinear hyperbolic systems of partial differential equations (PDE) on unstructured polygonal Voronoi meshes. Rather than using classical…

Numerical Analysis · Mathematics 2022-07-20 Walter Boscheri , Michael Dumbser , Elena Gaburro

In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier-Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with…

Numerical Analysis · Mathematics 2022-03-01 Yuhang Wang , Liang Pan

We develop a novel cut discontinuous Galerkin (CutDG) method for stationary advection-reaction problems on surfaces embedded in $\mathbb{R}^d$. The CutDG method is based on embedding the surface into a full-dimensional background mesh and…

Numerical Analysis · Mathematics 2023-04-13 Tale Bakken Ulfsby , André Massing , Simon Sticko

This paper presents a high-order discontinuous Galerkin finite element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced…

Numerical Analysis · Mathematics 2025-01-29 Laura Río-Martín , Michael Dumbser

In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the traditional method of lines framework and utilizes…

Numerical Analysis · Mathematics 2024-02-26 Qifan Chen , Zheng Sun , Yulong Xing

High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…

Numerical Analysis · Mathematics 2025-11-12 Patrick Kopper , Anna Schwarz , Jens Keim , Andrea Beck

Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…

Computational Physics · Physics 2020-02-03 Liang Chen , Hakan Bagci

Hydrodynamical numerical methods that converge with high-order hold particular promise for astrophysical studies, as they can in principle reach prescribed accuracy goals with higher computational efficiency than standard second- or…

Instrumentation and Methods for Astrophysics · Physics 2023-05-05 Miha Cernetic , Volker Springel , Thomas Guillet , Rüdiger Pakmor

We investigate two efficient time discretizations for the post-processing technique of discontinuous Galerkin (DG) methods to solve hyperbolic conservation laws. The post-processing technique, which is applied at the final time of the DG…

Numerical Analysis · Mathematics 2023-12-22 Xiaozhou Li

The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…

Numerical Analysis · Mathematics 2025-11-11 Maya Briani , Gabriella Puppo , Giuseppe Visconti

We propose an arbitrarily high-order globally divergence-free entropy stable nodal discontinuous Galerkin (DG) method to directly solve the conservative form of the ideal MHD equations using appropriate quadrature rules. The method ensures…

Numerical Analysis · Mathematics 2025-01-14 Yuchang Liu , Wei Guo , Yan Jiang , Mengping Zhang

In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is…

Numerical Analysis · Mathematics 2016-07-08 Wei Guo , Yingda Cheng

In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…

Numerical Analysis · Mathematics 2024-04-10 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not…

Numerical Analysis · Mathematics 2020-05-06 Andrew R. Winters , David A. Kopriva , Gregor J. Gassner , Florian Hindenlang

We present a Discontinuous Galerkin (DG) solver for the compressible Navier-Stokes system, designed for applications of technological and industrial interest in the subsonic region. More precisely, this work aims to exploit the…

Numerical Analysis · Mathematics 2025-08-26 Spiros Zafeiris , Emmanuil H. Georgoulis , George Papadakis

In this paper, we theoretically and numerically verify that the discontinuous Galerkin (DG) methods with central fluxes for linear hyperbolic equations on non-uniform meshes have sub-optimal convergence properties when measured in the…

Numerical Analysis · Mathematics 2020-03-03 Yong Liu , Chi-Wang Shu , Mengping Zhang

In this work, an exponential Discontinuous Galerkin (DG) method is proposed to solve numerically Vlasov type equations. The DG method is used for space discretization which is combined exponential Lawson Runge-Kutta method for time…

Numerical Analysis · Mathematics 2023-08-01 Nicolas Crouseilles , Xue Hong

We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…

Numerical Analysis · Mathematics 2024-09-27 Jau-Uei Chen , Tamás L. Horváth , Tan Bui-Thanh

We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…

Numerical Analysis · Mathematics 2026-01-29 Vit Dolejsi , Jakub Sistek