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.
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {48},
year = {2014},
pages = {859-874},
doi = {10.1051/m2an/2013123},
mrnumber = {3264337},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2014__48_3_859_0}
}
Burman, Erik; Hansbo, Peter. Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes' problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) pp. 859-874. doi : 10.1051/m2an/2013123. http://gdmltest.u-ga.fr/item/M2AN_2014__48_3_859_0/
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