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This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel…

Numerical Analysis · Mathematics 2019-08-16 Matteo Giacomini , Alexandros Karkoulias , Ruben Sevilla , Antonio Huerta

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$ for the…

Numerical Analysis · Mathematics 2019-02-26 Fei Wang , Shuonan Wu , Jinchao Xu

We present some new analytical tools for the error analysis of hybridizable discontinuous Galerkin (HDG) method for linear elasticity. These tools allow us to analyze more variants of HDG method using the projection-based approach, which…

Numerical Analysis · Mathematics 2019-10-22 Shukai Du , Francisco-Javier Sayas

We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and…

Numerical Analysis · Mathematics 2025-06-24 Salim Meddahi

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 consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that the iterative…

Numerical Analysis · Mathematics 2025-04-28 Simone Pescuma , Gwénaël Gabard , Théophile Chaumont-Frelet , Axel Modave

In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…

Numerical Analysis · Mathematics 2024-11-26 Shipra Gupta , Amiya Kumar Pani , Sangita Yadav

We develop and analyze a new hybridizable discontinuous Galerkin (HDG) method for solving third-order Korteweg-de Vries type equations. The approximate solutions are defined by a discrete version of a characterization of the exact solution…

Numerical Analysis · Mathematics 2026-05-25 Bo Dong

We propose and analyze a hybridized discontinuous Galerkin (HDG) method for the spherically symmetric Einstein--scalar system in Bondi gauge. After rewriting the model as a local first-order PDE--ODE system by introducing suitable scaled…

Numerical Analysis · Mathematics 2026-04-07 Mukul Dwivedi , Andreas Rupp

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

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…

Numerical Analysis · Mathematics 2019-08-20 Matteo Giacomini , Ruben Sevilla

The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…

Fluid Dynamics · Physics 2020-02-19 Wei Su , Peng Wang , Yonghao Zhang , Lei Wu

We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…

Numerical Analysis · Mathematics 2024-09-27 Jau-Uei Chen , Tamás L. Horváth , Tan Bui-Thanh

Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday's and…

Computational Engineering, Finance, and Science · Computer Science 2020-06-24 Luca Berardocco , Martin Kronbichler , Volker Gravemeier

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 a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate $\Omega$ by a…

Numerical Analysis · Mathematics 2021-07-29 Nestor Sánchez , Tonatiuh Sánchez-Vizuet , Manuel E. Solano

We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…

Computational Engineering, Finance, and Science · Computer Science 2018-02-19 Maurice S. Fabien , Matthew G. Knepley , Beatrice M. Riviere

This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary…

Numerical Analysis · Mathematics 2024-06-28 Xiaoqi Ma , Jin Zhang

A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…

Numerical Analysis · Mathematics 2025-05-19 Keegan L. A. Kirk , Beatrice Riviere

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

Numerical Analysis · Mathematics 2024-05-06 Andrew Ho , Uri Shumlak