Geodesic
Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes' problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 3, pp. 859-874

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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.

DOI : 10.1051/m2an/2013123
Classification : 65N12, 65N30
Keywords: finite element methods, stabilized methods, penalty methods, Stokes' problem, fictitious domain 
@article{M2AN_2014__48_3_859_0,
     author = {Burman, Erik and Hansbo, Peter},
     title = {Fictitious domain methods using cut elements: {III.} {A} stabilized {Nitsche} method for {Stokes'} problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {859--874},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     doi = {10.1051/m2an/2013123},
     mrnumber = {3264337},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013123/}
}
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Burman, Erik; Hansbo, Peter. Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes' problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 3, pp. 859-874. doi: 10.1051/m2an/2013123

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