WIAS Preprint No. 2874, (2021)

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



Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Moreau, Baptiste
  • Novo, Julia

2020 Mathematics Subject Classification

  • 65M60

Keywords

  • Convection-diffusion-reaction equations, convection-dominated regime, SUPG-ROM method, error analysis

DOI

10.20347/WIAS.PREPRINT.2874

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.

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