37 citations · 81 across the 22 of their papers we have counts for
22 papers
An Incremental SVD Method for Non-Fickian Flows in Porous Media: Addressing Storage and Computational Challenges
Gang Chen, Yangwen Zhang, Dujin Zuo
It is well known that the numerical solution of the Non-Fickian flows at the current stage depends on all previous time instances. Consequently, the storage requirement increases l…
Locking-free HDG methods for Reissner-Mindlin plates equations on polygonal meshes
Gang Chen, Lu Zhang, Shangyou Zhang
We present and analyze a new hybridizable discontinuous Galerkin method (HDG) for the Reissner-Mindlin plate bending system. Our method is based on the formulation utilizing Helmho…
Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations
Gang Chen, Xiaoping Xie
This paper analyzes a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stoke…
A New Global Divergence Free and Pressure-Robust HDG Method for Tangential Boundary Control of Stokes Equations
Gang Chen, Wei Gong, Mariano Mateos +2
In [ESAIM: M2AN, 54(2020), 2229-2264], we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optim…
Sharp estimates of HDG methods for Poisson equation II: 3D
Gang Chen, Peter Monk, Yangwen Zhang
In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal estimates (up to logarithmic factors) for the solution of Poisson's equation by a hybridizable discon…
Semi-discrete and fully discrete HDG methods for Burgers' equation
Zimo Zhu, Gang Chen, Xiaoping Xie
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 discret…
Superconvergent Interpolatory HDG methods for reaction diffusion equations II: HHO-inspired methods
Gang Chen, Bernardo Cockburn, John R Singler +1
In J. Sci. Comput., 81: 2188-2212, 2019, we considered a superconvergent hybridizable discontinuous Galerkin (HDG) method, defined on simplicial meshes, for scalar reaction diffusi…
norm error estimates for HDG methods applied to the Poisson equation with an application to the Dirichlet boundary control problem
Gang Chen, Peter Monk, Yangwen Zhang
We prove quasi-optimal norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) m…
HDG and CG methods for the Indefinite Time-Harmonic Maxwell's Equations under minimal regularity
Gang Chen, Peter Monk, Yangwen Zhang
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…
A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs
Gang Chen, Liangya Pi, Yangwen Zhang
We devised a first order time stepping ensemble hybridizable discontinuous Galerkin (HDG) method for a group of parameterized convection diffusion PDEs with different initial condi…
Superconvergent interpolatory HDG methods for reaction diffusion equations I: An HDG method
Gang Chen, Bernardo Cockburn, John Singler +1
In our earlier work [8], we approximated solutions of a general class of scalar parabolic semilinear PDEs by an interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG…
Superconvergent HDG methods for Maxwell's equations via the -decomposition
Gang Chen, Peter Monk, Yangwen Zhang
The concept of the -decomposition was introduced by Cockburn et al.\ in Math. Comp.\ vol.\ 86 (2017), pp.\ 1609-1641 {to provide criteria to guarantee optimal convergence rates…
A Superconvergent Ensemble HDG Method for Parameterized Convection Diffusion Equations
Gang Chen, Liangya Pi, Liwei Xu +1
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 h…
A hybridizable discontinuous Galerkin method for the quad-curl problem
Gang Chen, Jintao Cui, Liwei Xu
The quad-curl problem arises in magnetohydrodynamics, inverse electromagnetic scattering and transform eigenvalue problems. In this paper we investigate a hybridizable discontinuou…
On the superconvergence of a hydridizable discontinuous Galerkin method for the Cahn-Hilliard equation
Gang Chen, Daozhi Han, John Singler +1
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 o…
An HDG Method for Time-dependent Drift-Diffusion Model of Semiconductor Devices
Gang Chen, Peter Monk, Yangwen Zhang
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 nonli…
An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDE
Gang Chen, John Richard Singler, Yangwen Zhang
We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a \emph{convection dominated} Dirichlet boundary control problem. Dirichlet bound…
A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs
Gang Chen, Guosheng Fu, John Richard Singler +1
We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018…
Analysis of an interior penalty DG method for the quad-curl problem
Gang Chen, Weifeng Qiu, Liwei Xu
The quad-curl term is an essential part of the resistive magnetohydrodynamic (MHD) equation and the fourth order inverse electromagnetic scattering problem, which are both of great…
Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator
Gang Chen, Jintao Cui, Liwei Xu
In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the n…
An HDG Method for Distributed Control of Convection Diffusion PDEs
Weiwei Hu, Jiguang Shen, John R. Singler +2
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.…
Robust weak Galerkin finite element methods for linear elasticity with continuous displacement trace approximation
Gang Chen, Xiaoping Xie
This paper proposes and analyzes a class of new weak Galerkin (WG) finite element methods for 2- and 3-dimensional linear elasticity problems. The methods use discontinuous piecewi…