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Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem

Published online by Cambridge University Press:  22 April 2014

Erik Burman  and
Peter Hansbo
Erik Burman
Affiliation:
Department of Mathematics, University College London, UK-WC1E 6BT United Kingdom
Peter Hansbo
Affiliation:
Department of Mechanical Engineering, Jönköping University, 551 11 Jönköping, Sweden. peter.hansbo@jth.hj.se .
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Abstract

We extend our results on fictitious domain methods for Poisson’s problem to the case of incompressible elasticity, or Stokes’ problem. The mesh is not fitted to the domain boundary. Instead boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, i.e., those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered.

Keywords

Finite element methodsstabilized methodspenalty methodsStokes’ problemfictitious domain
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 3 , May 2014 , pp. 859 - 874
Copyright
© EDP Sciences, SMAI, 2014

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