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Mathematical analysis and approximation of a multiscale elliptic-parabolic system

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.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-68686
Date January 2018
CreatorsRichardson, Omar
PublisherKarlstads universitet, Institutionen för matematik och datavetenskap (from 2013), Karlstad
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeLicentiate thesis, monograph, info:eu-repo/semantics/masterThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess
RelationKarlstad University Studies, 1403-8099 ; 2018:33

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