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.
Mots-clés : 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://archive.numdam.org/articles/10.1051/m2an/2013123/}
}
TY - JOUR AU - Burman, Erik AU - Hansbo, Peter TI - Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes' problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 859 EP - 874 VL - 48 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2013123/ DO - 10.1051/m2an/2013123 LA - en ID - M2AN_2014__48_3_859_0 ER -
%0 Journal Article %A Burman, Erik %A Hansbo, Peter %T Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes' problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 859-874 %V 48 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2013123/ %R 10.1051/m2an/2013123 %G en %F 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 , Tome 48 (2014) no. 3, pp. 859-874. doi : 10.1051/m2an/2013123. http://archive.numdam.org/articles/10.1051/m2an/2013123/
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