English
Related papers

Related papers: A Discontinuous Galerkin method for Shock Capturin…

200 papers

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…

Numerical Analysis · Mathematics 2023-06-28 Stefano Bonetti , Michele Botti , Ilario Mazzieri , Paola F. Antonietti

We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite volume (FV) method. The strategy relies on a simple operator splitting…

Numerical Analysis · Mathematics 2020-02-10 Vincent Heningburg , Cory D. Hauck

The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The…

Numerical Analysis · Mathematics 2022-12-21 Thomas Roy , Julian Andrej , Victor A. Beck

We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…

Numerical Analysis · Mathematics 2018-12-11 Paola F. Antonietti , Francesco Bonaldi , Ilario Mazzieri

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection…

Numerical Analysis · Mathematics 2017-10-25 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

In this paper, we present a high-order finite element method based on a reconstructed approximation to the biharmonic equation. In our construction, the space is reconstructed from nodal values by solving a local least squares fitting…

Numerical Analysis · Mathematics 2024-07-08 Ruo Li , Qicheng Liu , Fanyi Yang

In this paper, we propose a high-order energy-conserving semi-Lagrangian discontinuous Galerkin(ECSLDG) method for the Vlasov-Ampere system. The method employs a semi-Lagrangian discontinuous Galerkin scheme for spatial discretization of…

Numerical Analysis · Mathematics 2025-04-30 Xiaofeng Cai , Qingtao Li , Hongtao Liu , Haibiao Zheng

We present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise linear polynomials. The goal is to allow for explicit time…

Numerical Analysis · Mathematics 2019-06-14 Christian Engwer , Sandra May , Andreas Nüßing , Florian Streitbürger

We propose and analyze discontinuous Galerkin (dG) approximations to 3D-1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D centerline. Convergence to weak solutions of a steady state…

Numerical Analysis · Mathematics 2023-12-29 Rami Masri , Miroslav Kuchta , Beatrice Riviere

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function…

Computational Physics · Physics 2017-01-06 Lukas Einkemmer , Matthias Wiesenberger

In this work we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such as exact mass conservation and…

Numerical Analysis · Mathematics 2016-12-06 Philip L. Lederer , Joachim Schöberl

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and…

Analysis of PDEs · Mathematics 2018-02-14 David Coulette , Emmanuel Franck , Philippe Helluy , Michel Mehrenberger , Laurent Navoret

Standard discontinuous Galerkin methods, based on piecewise polynomials of degree $ \qq=0,1$, are considered for temporal semi-discretization for second order hyperbolic equations. The main goal of this paper is to present a simple and…

Numerical Analysis · Mathematics 2022-10-19 Neda Rezaei , Fardin Saedpanah

A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a low-rank decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This…

Numerical Analysis · Mathematics 2025-08-25 Andres Galindo-Olarte , Joseph Nakao , Mirjeta Pasha , Jing-Mei Qiu , William Taitano

We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional…

Analysis of PDEs · Mathematics 2019-06-18 Cung The Anh , Tran Minh Nguyet

In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…

Numerical Analysis · Mathematics 2019-02-08 Giovanni Stabile , Gianluigi Rozza

This paper deals with the numerical resolution of kinetic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. We focus on the kinetic model considered in [18, 17] where alignment is…

Numerical Analysis · Mathematics 2017-05-24 Francis Filbet , Chi-Wang Shu

This work presents the discontinuous Galerkin discretization of the consistent splitting scheme proposed by Liu [J. Liu, J. Comp. Phys., 228(19), 2009]. The method enforces the divergence-free constraint implicitly, removing…

Numerical Analysis · Mathematics 2026-04-29 Dominik Still , Natalia Nebulishvili , Richard Schussnig , Katharina Kormann , Martin Kronbichler

Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits…

Computational Physics · Physics 2021-10-04 Zhuogang Peng , Ryan G. McClarren

High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…

Fluid Dynamics · Physics 2025-04-02 Anna Schwarz , Daniel Kempf , Jens Keim , Patrick Kopper , Christian Rohde , Andrea Beck