English
Related papers

Related papers: Coupling of HDG with a double-layer potential BEM

200 papers

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

In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs have different coefficients, initial conditions, source terms…

Numerical Analysis · Mathematics 2019-03-12 Gang Chen , Liangya Pi , Liwei Xu , Yangwen Zhang

We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduction of an HDG flux of the dual saddle-point form of the MHD…

Numerical Analysis · Mathematics 2019-01-15 Jeonghun J. Lee , Stephen Shannon , Tan Bui-Thanh , John N. Shadid

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

We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint…

Numerical Analysis · Mathematics 2025-02-18 Aycil Cesmelioglu , Miroslav Kuchta , Jeonghun J. Lee , Sander Rhebergen

We derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress…

Numerical Analysis · Mathematics 2016-11-18 Allan Hungria , Daniele Prada , Francisco-Javier Sayas

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

This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees $ k \ (k…

Numerical Analysis · Mathematics 2021-02-02 Zimo Zhu , Gang Chen , Xiaoping Xie

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

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 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 propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic convection diffusion PDE. We derive optimal a priori error estimates for the state,…

Numerical Analysis · Mathematics 2018-06-04 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng

We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…

Numerical Analysis · Mathematics 2026-04-24 Gang Chen , Daozhi Han , Jiaxuan Liu , Yangwen Zhang , Dujin Zuo

We consider a transmission problem consisting of a singularly perturbed reaction diffusion equation on a bounded domain and the Laplacian in the exterior, connected through standard transmission conditions. We establish a DPG scheme coupled…

Numerical Analysis · Mathematics 2016-09-21 Thomas Führer , Norbert Heuer

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

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

We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Sander Rhebergen , Garth N. Wells

We propose a new tool, which we call $M$-decompositions, for devising superconvergent hybridizable discontinuous Galerkin (HDG) methods and hybridized-mixed methods for linear elasticity with strongly symmetric approximate stresses on…

Numerical Analysis · Mathematics 2017-04-18 Bernardo Cockburn , Guosheng Fu

We present and analyze a discontinuous variant of the hp-version of the boundary element Galerkin method with quasi-uniform meshes. The model problem is that of the hypersingular integral operator on an (open or closed) polyhedral surface.…

Numerical Analysis · Mathematics 2012-06-28 Norbert Heuer , Salim Meddahi

We consider a distributed optimal control problem governed by an elliptic convection diffusion PDE, and propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. We use polynomials of degree $k+1$ and $k \ge 0$…

Numerical Analysis · Mathematics 2018-11-27 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng