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A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem

A. Massing ; M. G. Larson ; Anders Logg (Institutionen för matematiska vetenskaper, matematik) ; M. E. Rognes
Journal of Scientific Computing (0885-7474). Vol. 61 (2014), 3, p. 604-628.
[Artikel, refereegranskad vetenskaplig]

We present a novel finite element method for the Stokes problem on fictitious domains. We prove inf-sup stability, optimal order convergence and uniform boundedness of the condition number of the discrete system. The finite element formulation is based on a stabilized Nitsche method with ghost penalties for the velocity and pressure to obtain stability in the presence of small cut elements. We demonstrate for the first time the applicability of the Nitsche fictitious domain method to three-dimensional Stokes problems. We further discuss a general, flexible and freely available implementation of the method and present numerical examples supporting the theoretical results.

Nyckelord: Fictitious domain; Stokes problem; Stabilized finite element methods; Nitsche's method



Denna post skapades 2014-11-27.
CPL Pubid: 206769

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur