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In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [J. Jang, F. Li, J.-M. Qiu and T. Xiong, submitted, arxiv:1306.0227] for kinetic transport equations under a…

Numerical Analysis · Mathematics 2014-06-12 Juhi Jang , Fengyan Li , Jing-Mei Qiu , Tao Xiong

We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduction of an HDG flux of the dual saddle-point form of the MHD…

Numerical Analysis · Mathematics 2019-01-15 Jeonghun J. Lee , Stephen Shannon , Tan Bui-Thanh , John N. Shadid

The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a…

Numerical Analysis · Mathematics 2022-07-19 Rami Masri , Boqian Shen , Beatrice Riviere

The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding…

Fluid Dynamics · Physics 2024-03-11 Eric J. Ching , Andrew D. Kercher , Andrew Corrigan

We present improved $L^2$-error estimates on the time-integrated primal variable for the wave equation in its first-order formulation. The space discretization relies on a hybrid nonconforming method, such as the hybridizable discontinuous…

Numerical Analysis · Mathematics 2025-11-18 Bernardo Cockburn , Alexandre Ern , Rekha Khot

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical…

Numerical Analysis · Mathematics 2020-09-30 Andrea Bonito , Ricardo H. Nochetto , Dimitrios Ntogkas

This paper introduces a novel staggered discontinuous Galerkin (SDG) method tailored for solving elliptic equations on polytopal meshes. Our approach utilizes a primal-dual grid framework to ensure local conservation of fluxes,…

Numerical Analysis · Mathematics 2024-11-01 L. Chen , X. Huang , E. Park , R. Wang

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a…

Numerical Analysis · Mathematics 2018-10-09 Jay Gopalakrishnan , Paulina Sepulveda

We deal with the problem of reconstructing interfaces using complex geometrical optics solutions for the Maxwell system. The contributions are twofold. First, we justify the enclosure method for the impenetrable obstacle case avoiding any…

Analysis of PDEs · Mathematics 2013-10-25 Manas Kar , Mourad Sini

We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the…

Numerical Analysis · Mathematics 2023-07-06 Giselle Sosa Jones , Jeonghun J. Lee , Sander Rhebergen

We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree…

Numerical Analysis · Mathematics 2023-05-08 Yan Chen , Ruo Li , Qicheng Liu

In this paper, we propose a weak Galerkin (WG) finite element method for the Maxwell eigenvalue problem. By restricting subspaces, we transform the mixed form of Maxwell eigenvalue problem into simple elliptic equation. Then we give the WG…

Numerical Analysis · Mathematics 2024-05-24 Shusheng Li , Qilong Zhai

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The…

Plasma Physics · Physics 2016-08-24 John Loverich , Ammar Hakim , Uri Shumlak

In this paper, we develop a Discontinuous Galerkin (DG) method for solving H(curl)-elliptic hemivariational inequalities. By selecting an appropriate numerical flux, we construct an Interior Penalty Discontinuous Galerkin (IPDG) scheme. A…

Numerical Analysis · Mathematics 2026-04-21 Xiajie Huang , Fei Wang , Weimin Han , Min Ling

In this paper, we study arbitrary order extended finite element (XFE) methods based on two discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and three dimensions. Optimal error estimates in the…

Numerical Analysis · Mathematics 2016-04-22 Fei Wang , Yuanming Xiao , Jinchao Xu

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

Optimization and Control · Mathematics 2013-08-09 Tuğba Akman , Bülent Karasözen

Computational electrodynamics (CED), the numerical solution of Maxwell's equations, plays an incredibly important role in several problems in science and engineering. High accuracy solutions are desired, and the discontinuous Galerkin (DG)…

Numerical Analysis · Mathematics 2019-06-26 Arijit Hazra , Praveen Chandrashekar , Dinshaw S. Balsara

In this paper we present a new high order semi-implicit DG scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible…

Numerical Analysis · Mathematics 2024-02-13 M. Tavelli , W. Boscheri

We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…

Numerical Analysis · Mathematics 2024-11-07 Andrea Cangiani , Zhaonan Dong , Emmanuil H. Georgoulis

In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG…

Fluid Dynamics · Physics 2013-10-01 Peter Bastian