Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations

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Date
2021
Volume
2874
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov--Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. Numerical studies illustrate the performance of the SUPG-ROM method.

Description
Keywords
Convection-diffusion-reaction equations, convection-dominated regime, SUPG-ROM method, error analysis
Citation
John, V., Moreau, B., & Novo, J. (2021). Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations (Vol. 2874). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2874
License
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