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Adaptive variational multiscale methods

Axel Målqvist (Institutionen för matematiska vetenskaper, matematik)
Göteborg : Chalmers University of Technology, 2005. ISBN: 91-7291-654-0.- 138 s.
[Doktorsavhandling]

In this thesis we present a new adaptive multiscale method for solving elliptic partial differential equations. The method is based on numerical solution of decoupled local fine scale problems on patches. Critical parameters such as fine and coarse scale mesh size and patch size are tuned automatically by an adaptive algorithm based on a posteriori error estimates. We extend the method to a mixed formulation of the Poisson equation and derive error estimates in this case as well. We also present a framework for adaptivity based on a posteriori error estimates for multi-physics problems. We study a coupled flow and transport problem and derive an a posteriori error estimate for a linear functional by introducing two dual problems, one associated with the transport equation and one associated with the flow equation. We also apply this method to a model problem in oil reservoir simulation.

Nyckelord: finite element method, Galerkin, duality, a posteriori error estimation, adaptivity, variational multiscale method, mixed formulation, multi-physics, oil reservoir simulation



Denna post skapades 2005-12-03. Senast ändrad 2013-09-25.
CPL Pubid: 6683

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur

Examination

Datum: 2005-09-30
Tid: 10.00
Lokal: 10.00 Hörsalen, matematiskt centrum
Opponent: Dr. Knut-Andreas Lie, SINTEF, Norway

Ingår i serie

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie 2336