37 citations · 184 across the 24 of their papers we have counts for
25 papers
Sharp and unified error estimates for the nonsymmetric Nitsche method on convex polytopes
Gang Chen, Chaoran Liu, Yangwen Zhang
Nitsche's method weakly imposes Dirichlet boundary conditions, but its nonsymmetric variant has long shown a gap between theory and computation: the classical ~analysis under…
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…
A fast reduced order method for linear parabolic inverse source problems
Yuxuan Huang, Yangwen Zhang
In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical soluti…
An efficient and memory free algorithm for subdiffusion equation using incremental singular value decomposition
Jichun Li, Yangpeng Zhang, Yangwen Zhang
In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous…
An Improved Incremental Singular Value Decomposition and New Error Bounds
Yangwen Zhang
The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arit…
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…
A Spectral Target Signature for Thin Surfaces with Higher Order Jump Conditions
Fioralba Cakoni, Heejin Lee, Peter Monk +1
In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in , from scattering d…
Target signatures for thin surfaces
Fioralba Cakoni, Peter Monk, Yangwen Zhang
We investigate an inverse scattering problem for a thin inhomogeneous scatterer in R^m, m = 2,3, which we model as a m-1 dimensional open surface. The scatterer is referred to as a…
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…
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…
Interpolatory HDG Method for Parabolic Semilinear PDEs
Bernardo Cockburn, John Richard Singler, Yangwen Zhang
We propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an in…
Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system
Wei Gong, Weiwei Hu, Mariano Mateos +2
We consider an unconstrained tangential Dirichlet boundary control problem for the Stokes equations with an penalty on the boundary control. The contribution of this paper…
An EDG Method for Distributed Optimal Control of Elliptic PDEs
Xiao Zhang, Yangwen Zhang, John R. Singler
We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive op…
A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs I: High Regularity
Weiwei Hu, Mariano Mateos, John R. Singler +1
We propose a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a Dirichlet boundary control problem governed by an elliptic convection diffusion P…
A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity
Weiwei Hu, Mariano Mateos, John R. Singler +2
In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HD…
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.…
HDG-POD Reduced Order Model of the Heat Equation
Jiguang Shen, John R. Singler, Yangwen Zhang
We propose a new hybridizable discontinuous Galerkin (HDG) model order reduction technique based on proper orthogonal decomposition (POD). We consider the heat equation as a test p…
An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs
Xiao Zhang, Yangwen Zhang, John R. Singler
We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a…
A Superconvergent Hybridizable Discontinuous Galerkin Method for Dirichlet Boundary Control of Elliptic PDEs
Weiwei Hu, Jiguang Shen, John R. Singler +2
We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. Thes…