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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-68686 |
| Date | January 2018 |
| Creators | Richardson, Omar |
| Publisher | Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), Karlstad |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, monograph, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Karlstad University Studies, 1403-8099 ; 2018:33 |
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