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The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…

Computational Physics · Physics 2018-11-14 Wei Su , Peng Wang , Yonghao Zhang , Lei Wu

The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…

Numerical Analysis · Mathematics 2017-11-16 Xiao Zhang , Xiaoping Xie , Shiquan Zhang

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

Computational Physics · Physics 2018-11-30 Martin Vymazal , David Moxey , Chris Cantwell , Spencer Sherwin , Robert M. Kirby

This article introduces a weak Galerkin (WG) finite element method for linear elasticity interface problems on general polygonal/ployhedra partitions. The developed WG method has been proved to be stable and accurate with optimal order…

Numerical Analysis · Mathematics 2021-12-14 Chunmei Wang , Shangyou Zhang

We analyze a high order unfitted hybridizable discontinuous Galerkin (HDG) method for an optimal control problem governed by a convection-diffusion equation posed in a domain with piecewise-wise $\mathcal{C}^2$ boundary $\partial \Omega$.…

Numerical Analysis · Mathematics 2026-04-02 Esteban Henríquez , Manuel Solano

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of…

Numerical Analysis · Mathematics 2013-04-16 Andrea Cangiani , Emmanuil H. Georgoulis , Max Jensen

We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the $L^2$-orthogonal projection onto the approximate space for a numerical trace into all…

Numerical Analysis · Mathematics 2017-11-16 Issei Oikawa

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 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

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 study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous…

Numerical Analysis · Mathematics 2019-03-12 Gang Chen , Jintao Cui , Liwei Xu

In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…

Numerical Analysis · Mathematics 2026-05-28 Ruo Li , Qicheng Liu , Fanyi Yang , Shuhai Zhao

We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations,…

Numerical Analysis · Mathematics 2017-12-11 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng

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 propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the…

Numerical Analysis · Mathematics 2025-05-27 Juan Han , Haijun Wu , Yuanming Xiao

A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other…

Computational Physics · Physics 2019-10-30 Trevor Vincent , Harald P. Pfeiffer , Nils L. Fischer

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

This paper develops an hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD) flow. The HDG scheme uses piecewise polynomials of degrees…

Numerical Analysis · Mathematics 2025-01-03 Min Zhang , Zimo Zhu , Qijia Zhai , Xiaoping Xie

We introduce a pure--stress formulation of the elasticity eigenvalue problem with mixed boundary conditions. We propose an H(div)-based discontinuous Galerkin method that imposes strongly the symmetry of the stress for the discretization of…

Numerical Analysis · Mathematics 2022-05-06 Salim Meddahi

We introduce new hybridizable discontinuous Galerkin (HDG) methods for solving the two-dimensional vector Laplacian equation under three types of boundary conditions: electric, magnetic, and Dirichlet. The method is formulated on a…

Numerical Analysis · Mathematics 2026-04-08 Bernardo Cockburn , Cristhian Núñez , Manuel A. Sánchez