Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion Equations

2011/03/14 by Traian Iliescu, Zhu Wang, iliescu, Traian +1
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1103.2729

openalex publication_date 2011/03/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested for convection-dominated convection-diffusion equations. The numerical analysis of the finite element discretization of the model is presented. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.

Citations

• Galerkin proper orthogonal decomposition methods for parabolic problems
• GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS

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