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In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…

In this paper we propose a novel staggered discontinuous Galerkin method for the Brinkman problem on general quadrilateral and polygonal meshes. The proposed method is robust in the Stokes and Darcy limits, in addition, hanging nodes can be…

Numerical Analysis · Mathematics 2020-04-22 Lina Zhao , Eric Chung , Ming Fai Lam

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in $\mathbb{R}^2$. In order to apply the PWDG method, we introduce an artificial…

Numerical Analysis · Mathematics 2016-11-23 Shelvean Kapita , Peter Monk

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

A nodal Discontinuous Galerkin (DG) method is derived for the analysis of time-domain (TD) scattering from doubly periodic PEC/dielectric structures under oblique interrogation. Field transformations are employed to elaborate a formalism…

Computational Engineering, Finance, and Science · Computer Science 2015-06-17 Nicholas C. Miller , Andrew D. Baczewski , John D. Albrecht , Balasubramaniam Shanker

We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general…

Numerical Analysis · Mathematics 2023-11-28 Stefano Bonetti , Michele Botti , Paola F. Antonietti

We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial…

Numerical Analysis · Mathematics 2020-12-24 Paola F. Antonietti , Lorenzo Mascotto , Marco Verani , Stefano Zonca

We study discontinuous Galerkin approximations of the $p$--biharmonic equation from a variational perspective. We propose a discrete variational formulation of the problem based on a appropriate definition of a finite element Hessian and…

Numerical Analysis · Mathematics 2015-09-23 Tristan Pryer

This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest…

Numerical Analysis · Mathematics 2025-12-03 Paola F. Antonietti , Michele Botti , Alessandra Cancrini , Ilario Mazzieri

A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…

Numerical Analysis · Mathematics 2016-07-12 Shuqin Wang , Jinyun Yuan , Weihua Deng , Yujiang Wu

This work is concerned with implementing the hybridizable discontinuous Galerkin (HDG) method to solve the linear anisotropic elastic equation in the frequency domain. First-order formulation with the compliance tensor and Voigt notation…

Analysis of PDEs · Mathematics 2024-04-29 Ha Pham , Florian Faucher , Hélène Barucq

In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming…

Numerical Analysis · Mathematics 2022-12-13 Issei Oikawa

In this paper we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify the right hand side of the body force in the…

Numerical Analysis · Mathematics 2020-07-02 Lina Zhao , Eun-Jae Park , Eric Chung

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

Numerical Analysis · Mathematics 2024-05-06 Andrew Ho , Uri Shumlak

We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that…

Computational Engineering, Finance, and Science · Computer Science 2025-03-07 Maurice S. Fabien

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

The paper proposes and analyzes an efficient second-order in time numerical approximation for the Allen-Cahn equation, which is a second order nonlinear equation arising from the phase separation model. We firstly present a fully discrete…

Numerical Analysis · Mathematics 2017-12-11 Huanrong Li , Junzhao Hu

This paper introduces well-balanced path-conservative discontinuous Galerkin (DG) methods for two-layer shallow water equations, ensuring exactness for both still water and moving water equilibrium steady states. The approach involves…

Numerical Analysis · Mathematics 2024-03-19 Jiahui Zhang , Yinhua Xia , Yan Xu

This work concerns with the discontinuous Galerkin (DG)method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary…

Numerical Analysis · Mathematics 2015-06-11 Thi Hong Cam Luong , Christian Daveau