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Related papers: HDG methods for elastodynamics

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The first super-convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is…

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

This paper presents a new hybridizable discontinuous Galerkin (HDG) method for linear elasticity on general polyhedral meshes, based on a strong symmetric stress formulation. The key feature of this new HDG method is the use of a special…

Numerical Analysis · Mathematics 2016-02-24 Weifeng Qiu , Jiguang Shen , Ke Shi

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

In this paper, we develop hybridized discontinuous Galerkin (HDG) methods for poroelastic wave equations. We first rewrite the governing equations to a first-order symmetric hyperbolic system in order to use dual mixed formulations for…

Numerical Analysis · Mathematics 2026-05-08 Jeonghun J. Lee , Manuel A. Sanchez

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

A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard discontinuous Galerkin scheme with upwind numerical fluxes and…

Numerical Analysis · Mathematics 2023-09-11 A. Modave , T. Chaumont-Frelet

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

We propose to use a hybridizable discontinuous Galerkin (HDG) method combined with the continuous Galerkin (CG) method to approximate Maxwell's equations. We make two contributions in this paper. First, even though there are many papers…

Numerical Analysis · Mathematics 2020-02-17 Gang Chen , Peter Monk , Yangwen Zhang

An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The…

Numerical Analysis · Mathematics 2021-02-16 Yihui Han , Xiao-Ping Wang , 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

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 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

We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…

Computational Engineering, Finance, and Science · Computer Science 2019-05-01 Shinhoo Kang , Tan Bui-Thanh , Todd Arbogast

This study introduces a hybridizable discontinuous Galerkin (HDG) method for simulating low-frequency wave propagation in poroelastic media. We present a novel four-field variational formulation and establish its well-posedness and energy…

Numerical Analysis · Mathematics 2025-03-12 Salim Meddahi

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

This paper analyzes the error estimates of the hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation with high wave number in two and three dimensions. The approximation piecewise polynomial spaces we deal with are of…

Numerical Analysis · Mathematics 2012-07-17 Huangxin Chen , Peipei Lu , Xuejun Xu

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

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

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 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
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