Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
1 Department of Mathematics, University College London, UK-WC1E 6BT United Kingdom
2 Department of Mechanical Engineering, Jönköping University, 551 11 Jönköping, Sweden .
Received: 14 August 2012
Revised: 8 August 2013
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.
Mathematics Subject Classification: 65N12 / 65N30
Key words: Finite element methods / stabilized methods / penalty methods / Stokes’ problem / fictitious domain
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