A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems

Mario Ohlberger, Kathrin Smetana*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

3 Citations (Scopus)

Abstract

We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.

Original languageEnglish
Title of host publicationECCOMAS Thematic Conference - ADMOS 2011
Subtitle of host publicationInternational Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference
Pages343-354
Number of pages12
Publication statusPublished - 16 Aug 2012
Externally publishedYes
Event5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011 - Paris, France
Duration: 6 Jun 20118 Jun 2011
Conference number: 5

Conference

Conference5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011
Abbreviated titleADMOS 2011
CountryFrance
CityParis
Period6/06/118/06/11

Keywords

  • A posteriori error estimation
  • Adaptive modeling
  • Hierarchical model reduction
  • Model reduction
  • Reduced basis methods

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