Journal ArticleDOI
Galerkin proper orthogonal decomposition methods for parabolic problems
Karl Kunisch,Stefan Volkwein +1 more
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions
Julia Schleuss,Kathrin Smetana +1 more
TL;DR: In this article , a deterministic time point selection method based on DEIM is proposed to solve the problem of heterogeneous time-dependent problems, where leverage score sampling is employed.
Journal ArticleDOI
Burgers方程基于POD方法的降维CN有限元外推算法 A Reduced-Order CN Finite Element Extrapolating Algorithm Based on POD for Burgers Equation
TL;DR: In this article, a finite element reduced-order extrapolating algorithm with second-order accuracy based on proper orthogonal decomposition (POD) technique is established for two-dimensional Burgers equation.
Book ChapterDOI
Reduced Models for Liquid Food Packaging Systems
TL;DR: In this paper, the authors present a set of reduced numerical models that have been developed in the past few years to support the design of paperboard packaging systems, which can be used in the preliminary design phase or whenever very fast evaluations are required.
Journal ArticleDOI
A precision preserving Crank–Nicolson mixed finite element lowering dimension method for the unsteady conduction-convection problem
TL;DR: In this article , a precision preserving Crank-Nicolson (CN) mixed finite element (MFE) lowering dimension (PPCNMFELD) method was developed by using proper orthogonal decomposition.
Journal ArticleDOI
A data-driven model reduction method for parabolic inverse source problems and its convergence analysis
Zhiwen Zhang,Zheng, Zimu +1 more
TL;DR: In this article , a data-driven model reduction method was proposed to solve parabolic inverse source problems with uncertain data efficiently, which is referred to as the POD method, and an a posteriori algorithm was designed to find the optimal regularization parameter in the optimization problem without knowing the noise level.
References
More filters
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