This paper puts forth two new closure models for the proper orthogonal decomposition
reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale …

We propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG)
method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses …

The synthesis of a model‐based control structure for general linear dissipative distributed
parameter systems (DPSs) is explored in this manuscript. Discrete‐time distributed state …

For nonlinear reduced‐order models (ROMs), especially for those with high‐order
polynomial nonlinearities or nonpolynomial nonlinearities, the computational complexity still …

In our earlier work (Cockburn et al. in J Sci Comput 79 (3): 1777–1800, 2019), we
approximated solutions of a general class of scalar parabolic semilinear PDEs by an …

In this paper, we propose an augmented subspace based adaptive proper orthogonal
decomposition (POD) method for solving the time dependent partial differential equations …

Interpolation methods for nonlinear finite element discretizations are commonly used to
eliminate the computational costs associated with the repeated assembly of the nonlinear …

The solution of large-scale matrix algebraic Riccati equations is important for instance in
control design and model reduction and remains an active area of research. We consider a …

This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers
equation is motivated by the Boussinesq equations that are often used to model the thermal …

Proper orthogonal decomposition (POD) is frequently applied to estimate parameters of
partial differential equations. This study examines the application of the POD method in …