English
Related papers

Related papers: A Superconvergent Ensemble HDG Method for Paramete…

200 papers

A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is…

Computational Engineering, Finance, and Science · Computer Science 2023-06-21 Ran Zhao , Ming Dong , Liang Chen , Jun Hu , Hakan Bagci

We present scalable iterative solvers and preconditioning strategies for Hybridizable Discontinuous Galerkin (HDG) discretizations of partial differential equations (PDEs) on graphics processing units (GPUs). The HDG method is implemented…

Numerical Analysis · Mathematics 2025-12-16 Andrew Welter , Ngoc Cuong Nguyen

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

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

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

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

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 propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an interpolation procedure to efficiently and accurately…

Numerical Analysis · Mathematics 2019-05-21 Bernardo Cockburn , John Richard Singler , Yangwen Zhang

In this paper, we develop a new discontinuous Galerkin method for solving several types of partial differential equations (PDEs) with high order spatial derivatives. We combine the advantages of local discontinuous Galerkin (LDG) method and…

Numerical Analysis · Mathematics 2020-03-13 Qi Tao , Yan Xu , Chi-Wang Shu

This work proposes a unified $hp$-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified $hp$-HDG…

Numerical Analysis · Mathematics 2023-12-22 Jau-Uei Chen , Shinhoo Kang , Tan Bui-Thanh , John N. Shadid

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 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

We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…

Numerical Analysis · Mathematics 2018-03-29 Philip L. Lederer , Christoph Lehrenfeld , Joachim Schöberl

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

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 propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several…

Numerical Analysis · Mathematics 2018-05-23 Sriramkrishnan Muralikrishnan , Minh-Binh Tran , Tan Bui-Thanh

We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…

Numerical Analysis · Mathematics 2024-12-20 Chunmei Wang , Ludmil Zikatanov

This paper analyzes a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the…

Numerical Analysis · Mathematics 2022-04-08 Gang Chen , Xiaoping Xie

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

Computational Physics · Physics 2018-11-30 Martin Vymazal , David Moxey , Chris Cantwell , Spencer Sherwin , Robert M. Kirby

We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…

Numerical Analysis · Mathematics 2026-04-27 Kersten Schmidt , Timon Seibel , Sebastian Schöps