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In this paper, we analyze a hybridized discontinuous Galerkin(HDG) method with reduced stabilization for the Stokes equations. The reduced stabilization enables us to reduce the number of facet unknowns and improve the computational…

Numerical Analysis · Mathematics 2015-08-12 Issei Oikawa

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

With increasing quantity and quality of solar observations, it becomes essential to account for three-dimensional heterogeneities in wave modeling for seismic data interpretation. In this context, we present a 3D solver of the time-harmonic…

In this paper, we develop a new discontinuous Galerkin method for solving several types of partial differential equations (PDEs) with high order spatial derivatives. We combine the advantages of local discontinuous Galerkin (LDG) method and…

Numerical Analysis · Mathematics 2020-03-13 Qi Tao , Yan Xu , Chi-Wang Shu

This paper analyzes a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the…

Numerical Analysis · Mathematics 2022-04-08 Gang Chen , Xiaoping Xie

Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve such PDEs involving space and time variables arising from wave propagation phenomena in important applications in science and engineering. To support an…

Computational Geometry · Computer Science 2008-04-08 Shripad Thite

We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG) methods, including both the primal and mixed formulations, for the approximation of a linear second-order elliptic problem on conforming simplicial…

Numerical Analysis · Mathematics 2017-06-20 Mark Ainsworth , Guosheng Fu

In this paper we propose and analyze a new coupling procedure for the Hybridizable Discontinuous Galerkin Method with Galerkin Boundary Element Methods based on a double layer potential representation of the exterior component of the…

Numerical Analysis · Mathematics 2012-12-11 Zhixing Fu , Norbert Heuer , Francisco-Javier Sayas

In this work we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the $L^2$ product in each cell of the discretization, we are able to…

Numerical Analysis · Mathematics 2023-04-13 Wenyu Lei , Stefano Piani , Patricio Farrell , Nella Rotundo , Luca Heltai

We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resulting discrete eigenproblem does not fit in the standard spectral approximation framework…

Numerical Analysis · Mathematics 2018-01-29 Felipe Lepe , Salim Meddahi , David Mora , Rodolfo Rodríguez

We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of divergence is imposed on the electric field. Then a Lagrange…

Numerical Analysis · Mathematics 2016-05-10 Huangxin Chen , Weifeng Qiu , Ke Shi

In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equation when upwind fluxes are used. We prove, for any polynomial degree $k$, the $2k+1$th (or $2k+1/2$th)…

Numerical Analysis · Mathematics 2013-11-28 Cao Waixiang , Zhang Zhimin , Zou Qingsong

We develop and analyze a local discontinuous Galerkin (LDG) method for solving integral fractional Laplacian problems on bounded Lipschitz domains. The method is based on a three-field mixed formulation involving the primal variable, its…

Numerical Analysis · Mathematics 2025-12-16 Rubing Han , Shuonan Wu , Hao Zhou

The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of the convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost $O(N^{-(k+1/2)})$ (up to a…

Numerical Analysis · Mathematics 2022-10-25 Li Yan , Zhoufeng Wang , Yao Cheng

We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…

Numerical Analysis · Mathematics 2026-04-27 Kersten Schmidt , Timon Seibel , Sebastian Schöps

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinear form is simplified without the need of the skeletal…

Numerical Analysis · Mathematics 2023-05-11 Yingying Xie , Shuhao Cao , Long Chen , Liuqiang Zhong

The concept of the $M$-decomposition was introduced by Cockburn et al.\ in Math. Comp.\ vol.\ 86 (2017), pp.\ 1609-1641 {to provide criteria to guarantee optimal convergence rates for the Hybridizable Discontinuous Galerkin (HDG) method for…

Numerical Analysis · Mathematics 2019-05-20 Gang Chen , Peter Monk , Yangwen Zhang

A scheme for the solution of fluid-structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid…

The $hp$ local discontinuous Galerkin (LDG) method proposed by Castillo et al. [Math. Comp.,~71 (238): 455-478, 2002] has been shown to be an efficient approach for solving convection-diffusion equations. However, theoretical analysis…

Numerical Analysis · Mathematics 2026-03-05 Wenjie Liu , Ruiyi Xie , Li-Lian Wang , Zhimin Zhang

This paper presents a generalized weak Galerkin (gWG) finite element method for linear elasticity problems on general polygonal and polyhedral meshes. The proposed framework is flexible and efficient, allowing for the use of nonpolynomial…

Numerical Analysis · Mathematics 2026-01-27 Junping Wang , Yue Wang