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The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…

Numerical Analysis · Mathematics 2014-10-07 Antonio Márquez , Salim Meddahi , Thanh Tran

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…

Computational Physics · Physics 2021-05-28 Tonatiuh Sánchez-Vizuet , Manuel E. Solano , Antoine J. Cerfon

We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model. With a special choice of velocity and pressure spaces…

Numerical Analysis · Mathematics 2024-12-20 Eric L. Peters , John A. Evans

This paper presents a high-order accurate Continuous Galerkin Finite Element Method (CGFEM) for solving the initial boundary value problems governed by the Incompressible Navier-Stokes (INS) equations. We discretize the INS equations using…

Numerical Analysis · Mathematics 2026-04-27 Mrityunjoy Mandal , Arnaud G Malan , Prince Nchupang , Jan Nordström

The development and application of the Discontinuous Galerkin (DG) method have attracted great attention in computational fluid dynamics (CFD) com- munity in the past decades. The underlying reason for such an intensive investigation is due…

Numerical Analysis · Mathematics 2016-01-20 Kun Xu , Chang Liu , Xiaodong Ren

Approximate approach based on the Galerkin method is suggested for the investigation of equilibrium stellar models, a relativistic collapse problem and black hole formation. Some results of its simplified version - energetic method- are…

Astrophysics · Physics 2007-05-23 G. S. Bisnovatyi-Kogan , A. V. Dorodnitsyn

In this paper, we develop sparse grid central discontinuous Galerkin (CDG) scheme for linear hyperbolic systems with variable coefficients in high dimensions. The scheme combines the CDG framework with the sparse grid approach, with the aim…

Numerical Analysis · Mathematics 2019-01-16 Zhanjing Tao , Anqi Chen , Mengping Zhang , Yingda Cheng

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are…

Numerical Analysis · Mathematics 2024-04-12 Tarik Dzanic

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

In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…

Numerical Analysis · Mathematics 2021-09-01 Roberto J. Cier , Sergio Rojas , Victor M. Calo

We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special…

Numerical Analysis · Mathematics 2023-03-10 Zhiming Chen , Yong Liu

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

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 paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial…

Numerical Analysis · Mathematics 2015-07-14 Liangliang Qiu , Weihua Deng , Jan Hesthaven

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

Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…

Numerical Analysis · Mathematics 2013-10-24 Yingda Cheng , Irene M. Gamba , Fengyan Li , Philip J. Morrison

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic…

Computational Physics · Physics 2016-09-30 F. Fillion-Gourdeau , E. Lorin , A. D. Bandrauk

In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete…

Numerical Analysis · Mathematics 2015-01-21 Paola F. Antonietti , Maurizio Grasselli , Simone Stangalino , Marco Verani

The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite…

Numerical Analysis · Mathematics 2023-12-18 Frederic Hecht , Olivier Pironneau

We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard…

Numerical Analysis · Mathematics 2021-07-23 Federico Vismara , Tommaso Benacchio , Luca Bonaventura