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We propose a hybridizable discontinuous Galerkin (HDG) finite element method to approximate the solution of the time dependent drift-diffusion problem. This system involves a nonlinear convection diffusion equation for the electron…

Numerical Analysis · Mathematics 2018-11-27 Gang Chen , Peter Monk , Yangwen Zhang

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

A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and…

Numerical Analysis · Mathematics 2022-09-07 Jiansong Zhang , Yun Yu , Jiang Zhu , Rong Qin , Yue Yu , Maosheng Jiang

In this paper, we perform non-linear minimization using the Hybridizable Discontinuous Galerkin method (HDG) for the discretization of the forward problem, and implement the adjoint-state method for the computation of the functional…

Analysis of PDEs · Mathematics 2020-09-10 Florian Faucher , Otmar Scherzer

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

We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…

Numerical Analysis · Mathematics 2014-09-26 Bernardo Cockburn , Kassem Mustapha

A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CG-HDG coupling exploits the…

Numerical Analysis · Mathematics 2020-01-29 Andrea La Spina , Matteo Giacomini , Antonio Huerta

In this work, a novel analysis of a hybrid discontinuous Galerkin method for the Helmholtz equation is presented. It uses wavenumber, mesh size and polynomial degree independent stabilisation parameters leading to impedance traces between…

Numerical Analysis · Mathematics 2023-07-11 Michael Leumüller , Joachim Schöberl

We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…

Numerical Analysis · Mathematics 2013-10-11 T. P. Barrios , R. Bustinza , V. Dominguez

A hybridizable discontinuous Galerkin (HDG) formulation of the linearized incompressible Navier-Stokes equations, known as Oseen equations, is presented. The Cauchy stress formulation is considered and the symmetry of the stress tensor and…

Numerical Analysis · Mathematics 2020-09-10 Matteo Giacomini , Ruben Sevilla , Antonio Huerta

The hybrid Raviart-Thomas mixed discontinuous Galerkin (HRTMDG) method is proposed for solving the Helmholtz equation. With a new energy norm, we establish the existence and uniqueness of the HRTMDG method, and give its convergence…

Numerical Analysis · Mathematics 2020-09-04 Jiansong Zhang , Jiang Zhu

The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the numerical solution is obtained. The scheme is proved to be…

Numerical Analysis · Mathematics 2023-02-28 Keegan L. A. Kirk , Rami Masi , Beatrice Riviere

New hybridized discontinuous Galerkin (HDG) methods for the interface problem for elliptic equations are proposed. Unknown functions of our schemes are $u_h$ in elements and $\hat{u}_h$ on inter-element edges. That is, we formulate our…

Numerical Analysis · Mathematics 2020-01-24 Masasru Miyashita , Norikazu Saito

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 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

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…

In this paper, we present an adaptive hybridizable $C^0$ discontinuous Galerkin (HCDG) method for Kirchhoff plates. A reliable and efficient a posteriori error estimator is produced for this HCDG method. Quasi-orthogonality and discrete…

Numerical Analysis · Mathematics 2016-08-08 Pengtao Sun , Xuehai Huang

This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary condition in the three dimensional…

Numerical Analysis · Mathematics 2012-12-11 Xiaobing Feng , Haijun Wu

In this article, we study the damped time-harmonic Galbrun's equation which models solar and stellar oscillations. We introduce and analyze hybrid discontinuous Galerkin discretizations (HDG) that are stable and optimally convergent for all…

Numerical Analysis · Mathematics 2025-11-17 Martin Halla , Christoph Lehrenfeld , Tim van Beeck

This work is concerned with implementing the hybridizable discontinuous Galerkin (HDG) method to solve the linear anisotropic elastic equation in the frequency domain. First-order formulation with the compliance tensor and Voigt notation…

Analysis of PDEs · Mathematics 2024-04-29 Ha Pham , Florian Faucher , Hélène Barucq