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math.NA2023
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…
math.NA2023
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…
math.NA2023
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…