Journal ArticleDOI
Galerkin proper orthogonal decomposition methods for parabolic problems
Karl Kunisch,Stefan Volkwein +1 more
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In this article, error bounds for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are proved and the resulting error bounds depend on the number of POD basis functions and on the time discretization.Abstract:
In this work error estimates for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are proved. The resulting error bounds depend on the number of POD basis functions and on the time discretization. Numerical examples are included.read more
Citations
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Journal ArticleDOI
Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
TL;DR: In this article, the authors proposed new Lagrangian inner products that are used together with Eulerian and Lagrangians data to construct a new projection-based reduced order model (ROM) basis.
Posted Content
A-posteriori snapshot location for POD in optimal control of linear parabolic equations
TL;DR: In this article, the approximation of an optimal control problem for linear PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR) is studied.
Reducing Memory Requirements in Scientific Computing and Optimal
TL;DR: Various techniques to reduce the memory requirements of high accuracy numerical simulations are discussed, focusing first on the storage of the solution data, which are typically double precision floating point values.
Dissertation
Estudio numérico del atractor en ecuaciones de navier-stokes aplicadas a modelos de circulación del océano
TL;DR: In this article, a nuevo modelo barotropico de circulacion del oceano is presented, where the main caracteristica se centra en retener el efecto que la batimetria ejerce sobre the dinamica de los oceanos.
References
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Book
Infinite-Dimensional Dynamical Systems in Mechanics and Physics
TL;DR: In this article, the authors give bounds on the number of degrees of freedom and the dimension of attractors of some physical systems, including inertial manifolds and slow manifolds.
Book
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Book
Galerkin Finite Element Methods for Parabolic Problems
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
Journal ArticleDOI
Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
Karl Kunisch,Stefan Volkwein +1 more
TL;DR: POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation to comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system.
Related Papers (5)
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
Karl Kunisch,Stefan Volkwein +1 more