8 papers
Penalized Weighted Trace Minimization for Optimal Control Device Design and Placement
James Cheung
In this paper, we present a new analytical framework for determining the well-posedness of constrained optimization problems that arise in the study of optimal control device desig…
Well-Posedness of the Bochner Integral Form of Operator-Valued Riccati Equations
James Cheung
In this short paper, we prove that the Bochner integral form of the operator-valued Riccati equation has a unique solution if and only if its mild form has a unique solution. This…
On the Approximation of Operator-Valued Riccati Equations in Hilbert Spaces
James Cheung
In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here that the error of the approx…
Enforcing Neumann Boundary Conditions with Polynomial Extension Operators to Acheive Optimal Convergence Rates on Polytopial Meshes in the Finite Element Method
James Cheung
In \cite{cheung2019optimally}, the authors presented two finite element methods for approximating second order boundary value problems on polytopial meshes with optimal accuracy wi…
Approximation of Algebraic Riccati Equations with Generators of Noncompact Semigroups
James Cheung
In this work, we demonstrate that the Bochner integral representation of the Algebraic Riccati Equations (ARE) are well-posed without any compactness assumptions on the coefficient…
A Coupling Approach for Linear Elasticity Problems with Spatially Noncoincident Interfaces
Pavel Bochev, James Cheung, Max Gunzburger +1
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we de…
Optimally accurate higher-order finite element methods on polytopial approximations of domains with smooth boundaries
James Cheung, Mauro Perego, Pavel Bochev +1
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the dom…
An Optimally Convergent Coupling Approach for Interface Problems Approximated with Higher-Order Finite Elements
Pavel Bochev, James Cheung, Max Gunzburger +1
In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagran…