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Mathematical analysis and approximation of a multiscale elliptic-parabolic system
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). (Applied Analysis)ORCID iD: 0000-0002-2185-641x
2018 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

We study a two-scale coupled system consisting of a macroscopic elliptic equation and a microscopic parabolic equation. This system models the interplay between a gas and liquid close to equilibrium within a porous medium with distributed microstructures. We use formal homogenization arguments to derive the target system. We start by proving well-posedness and inverse estimates for the two-scale system. We follow up by proposing a Galerkin scheme which is continuous in time and discrete in space, for which we obtain well-posedness, a priori error estimates and convergence rates. Finally, we propose a numerical error reduction strategy by refining the grid based on residual error estimators.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2018. , p. 74
Series
Karlstad University Studies, ISSN 1403-8099 ; 2018:33
Keywords [en]
Two-scale modelling, two-scale Galerkin approximation, inverse Robin estimates, elliptic-parabolic system, a priori analysis, a posteriori error estimators
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-68686ISBN: 978-91-7063-867-1 (print)ISBN: 978-91-7063-962-3 (electronic)OAI: oai:DiVA.org:kau-68686DiVA, id: diva2:1237656
Presentation
2018-09-05, 1B306, Fryxellsalen, Universitetsgatan 2, Karlstad, 10:00 (English)
Opponent
Supervisors
Available from: 2018-08-17 Created: 2018-08-09 Last updated: 2018-10-23Bibliographically approved

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Richardson, Omar

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CiteExportLink to record
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Citation style
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Language
  • de-DE
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Output format
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