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We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection-diffusion problem within a more general Friedrichs system framework. With carefully constructed numerical traces, we introduce…

Numerical Analysis · Mathematics 2023-06-01 Jindong Wang , Shuonan Wu

In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…

Numerical Analysis · Mathematics 2022-04-06 Aikaterini Aretaki , Efthymios N. Karatzas , Georgios Katsouleas

We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…

Numerical Analysis · Mathematics 2022-01-07 Thad A. Gleason , Eric L. Peters , John A. Evans

Plasmonic nanostructures significantly improve the performance of photoconductive devices (PCDs) in generating terahertz radiation. However, they are geometrically intricate and result in complicated electromagnetic (EM) field and carrier…

Numerical Analysis · Mathematics 2020-10-14 Liang Chen , Hakan Bagci

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

We propose a hydridizable discontinuous Galerkin (HDG) method for solving the Cahn-Hilliard equation. The temporal discretization can be based on either the backward Euler method or the convex-splitting method. We show that the fully…

Numerical Analysis · Mathematics 2024-12-20 Gang Chen , Daozhi Han , John Singler , Yangwen Zhang

We propose a generalized Eulerian-Lagrangian (GEL) discontinuous Galerkin (DG) method. The method is a generalization of the Eulerian-Lagrangian (EL) DG method for transport problems proposed in [arXiv preprint arXiv: 2002.02930 (2020)],…

Numerical Analysis · Mathematics 2022-06-08 Xue Hong , Jing-Mei Qiu

We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem…

Numerical Analysis · Mathematics 2016-01-21 Peipei Lu , Huangxin Chen , Weifeng Qiu

In this paper, we develop a high order structure-preserving local discontinuous Galerkin (DG) scheme for the compressible self-gravitating Euler equations, which pose great challenges due to the presence of time-dependent gravitational…

Numerical Analysis · Mathematics 2025-10-07 Liang Pan , Wei Chen , Jianxian Qiu , Tao Xiong

We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate $\Omega$ by a…

Numerical Analysis · Mathematics 2021-07-29 Nestor Sánchez , Tonatiuh Sánchez-Vizuet , Manuel E. Solano

The discontinuous Galerkin dG method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily…

Numerical Analysis · Mathematics 2022-08-09 William McLean

This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or…

Numerical Analysis · Mathematics 2023-04-27 Liya Gaynutdinova , Martin Ladecký , Ivana Pultarová , Miloslav Vlasák , Jan Zeman

In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…

Numerical Analysis · Mathematics 2024-11-26 Shipra Gupta , Amiya Kumar Pani , Sangita Yadav

This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…

Analysis of PDEs · Mathematics 2019-11-26 B. J. Grieshaber , F. Rasolofoson , B. D. Reddy

We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly…

Numerical Analysis · Mathematics 2020-09-25 Qiwei Sheng , Cory D. Hauck

Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed…

Numerical Analysis · Mathematics 2019-02-26 Qiang Du , Xiaobo Yin

We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is to provide a critical assessment of the computational…

Computational Engineering, Finance, and Science · Computer Science 2014-11-12 Michael Woopen , Aravind Balan , Georg May , Jochen Schütz

In this paper we investigate the superconvergence properties of the discontinuous Galerkin method based on the upwind-biased flux for linear time-dependent hyperbolic equations. We prove that for even-degree polynomials, the method is…

Numerical Analysis · Mathematics 2016-02-23 Daniel Frean , Jennifer Ryan

In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber…

Numerical Analysis · Mathematics 2024-11-26 Gang Chen , Haijun Wu , Liwei Xu

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

Numerical Analysis · Mathematics 2016-06-22 Maurizio Tavelli , Michael Dumbser