37 citations · 217 across the 22 of their papers we have counts for
24 papers
A New Proper Orthogonal Decomposition Method with Second Difference Quotients for the Wave Equation
Andrew Janes, John R. Singler
Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduc…
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 new approach to proper orthogonal decomposition with difference quotients
Sarah K. Locke, John R. Singler
In a recent work [B. Koc et al., arXiv:2010.03750, SIAM J. Numer. Anal., to appear], the authors showed that including difference quotients (DQs) is necessary in order to prove opt…
Analysis and approximations of Dirichlet boundary control of Stokes flows in the energy space
W. Gong, M. Mateos, J. Singler +1
We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the norm a…
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition
Birgul Koc, Samuele Rubino, Michael Schneier +2
In this paper, we resolve several long standing issues dealing with optimal pointwise in time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the h…
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…
New proper orthogonal decomposition approximation theory for PDE solution data
Sarah Locke, John Singler
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking val…
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…
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 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…
A note on incremental POD algorithms for continuous time data
Hiba Fareed, John R. Singler
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of P…
Error Analysis of an Incremental POD Algorithm for PDE Simulation Data
Hiba Fareed, John R. Singler
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we proposed an incremental SVD algorithm with respect to a weighted inner product to compute t…
Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping
Belinda A. Batten, Hesam Shoori, John R. Singler +1
We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a ti…
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…
A Superconvergent HDG Method for Distributed Control of Convection Diffusion PDEs
Weiwei Hu, Jiguang Shen, John R. Singler +2
We consider a distributed optimal control problem governed by an elliptic convection diffusion PDE, and propose a hybridizable discontinuous Galerkin (HDG) method to approximate th…