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A linear semi-implicit hybridizable discontinuous Galerkin (HDG) scheme is proposed to solve the diffusive Peterlin viscoelastic model, allowing the diffusion coefficient $\ep$ of the conformation tensor to be arbitrarily small. We…

Numerical Analysis · Mathematics 2025-03-12 Sibang Gou , Jingyan Hu , Qi Wang , Feifei Jing , Guanyu Zhou

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

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

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

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

Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by…

Numerical Analysis · Mathematics 2024-01-05 Shixin Xu , Zhiliang 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

The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at…

Numerical Analysis · Mathematics 2025-05-08 Ari E. Rappaport , Théophile Chaumont-Frelet , Axel Modave

We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…

Numerical Analysis · Mathematics 2013-10-11 Yalchin Efendiev , Raytcho Lazarov , Ke Shi

In our earlier work [8], we approximated solutions of a general class of scalar parabolic semilinear PDEs by an interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method. This method reduces the computational cost…

Numerical Analysis · Mathematics 2021-02-01 Gang Chen , Bernardo Cockburn , John Singler , Yangwen Zhang

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 macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we investigate the performance of the macro-element HDG method…

Computational Engineering, Finance, and Science · Computer Science 2024-02-27 Vahid Badrkhani , Marco F. P. ten Eikelder , Rene R. Hiemstra , Dominik Schillinger

The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light…

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

This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG…

Numerical Analysis · Mathematics 2022-02-08 Juan M. Cardenas , Manuel Solano

We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\alpha<1$. For each time $t \in [0,T]$, the HDG approximations are taken to…

Numerical Analysis · Mathematics 2014-12-08 Kassem Mustapha , Maher Nour , Bernardo Cockburn

We propose a hydridizable discontinuous Galerkin (HDG) method for solving the Cahn-Hilliard equation. The temporal discretization can be based on either the backward Euler method or the convex-splitting method. We show that the fully…

Numerical Analysis · Mathematics 2024-12-20 Gang Chen , Daozhi Han , John Singler , Yangwen Zhang

We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…

Numerical Analysis · Mathematics 2017-07-10 Andre Massing

We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source term and the diffusion coefficient are non-linear. We…

Numerical Analysis · Mathematics 2021-12-30 Nestor Sánchez , Tonatiuh Sánchez-Vizuet , Manuel E. Solano

A concise Matlab implementation of a stable parallelizable space-time Petrov-Galerkin discretization for parabolic evolution equations is given. Emphasis is on reusability of spatial finite element codes.

Numerical Analysis · Mathematics 2015-06-19 Roman Andreev