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| File | Size | Format | |
|---|---|---|---|
| wias_preprints_2874.pdf | 1,22 MB | Adobe PDF | View/Open |
| Title: | Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations |
| Authors: | John, Volker; Moreau, Baptiste; Novo, Julia |
| Publishers version: | https://doi.org/10.20347/WIAS.PREPRINT.2874 |
| URI: | https://oa.tib.eu/renate/handle/123456789/9592 https://doi.org/10.34657/8630 |
| Issue Date: | 2021 |
| Journal: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Volume: | 2874 |
| 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. |
| Keywords: | Convection-diffusion-reaction equations; convection-dominated regime; SUPG-ROM method; error analysis |
| Type: | report; Text |
| Publishing status: | publishedVersion |
| DDC: | 510 |
| License: | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. |
| Appears in Collections: | Mathematik |
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John, Volker, Baptiste Moreau and Julia Novo, 2021. Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
John, V., Moreau, B. and Novo, J. (2021) Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. doi: https://doi.org/10.20347/WIAS.PREPRINT.2874.
John V, Moreau B, Novo J. Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations. Vol. 2874. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2021.
John, V., Moreau, B., & Novo, J. (2021). Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations (Version publishedVersion, Vol. 2874). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org/https://doi.org/10.20347/WIAS.PREPRINT.2874
John V, Moreau B, Novo J. Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations. Vol. 2874. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2021. doi:https://doi.org/10.20347/WIAS.PREPRINT.2874
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