Related papers: Pointwise error bounds in POD methods without diff…

In a recent work [B. Koc et al., arXiv:2010.03750, SIAM J. Numer. Anal., to appear], the authors showed that including difference quotients (DQs) is necessary in order to prove optimal pointwise in time error bounds for proper orthogonal…

Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In a…

While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…

In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in [26]. In particular, we study the behavior of the…

Proper orthogonal decomposition methods for model reduction utilize information about the solution at certain time and parameter points to generate a reduced space basis. In this paper, we compare two proper orthogonal decomposition methods…

This paper presents a theoretical and numerical investigation of the following practical question: Should the time difference quotients of the snapshots be used to generate the proper orthogonal decomposition basis functions? The answer to…

Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are considered and analyzed. We consider two cases, the case in which the snapshots are based on a non inf-sup stable method and the case in which the…

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully-discrete…

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…

In this paper, we resolve several long standing issues dealing with optimal pointwise in time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heat equation. In particular, we study the role played by…

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…

In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain…

Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral…

In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a…