We develop a Nitsche fictitious domain method for the Stokes problem starting
from a stabilized Galerkin finite element method with low order elements for
both the velocity and the pressure. By introducing additional penalty terms for
the jumps in the normal velocity and pressure gradients in the vicinity of the
boundary, we show that the method is inf-sup stable. As a consequence, optimal
order a priori error estimates are established. Moreover, the condition number
of the resulting stiffness matrix is shown to be bounded independently of the
location of the boundary. We discuss a general, flexible and freely available
implementation of the method in three spatial dimensions and present numerical
examples supporting the theoretical results.
%0 Generic
%1 citeulike:14289407
%A Massing, Andre
%A Larson, Mats G.
%A Logg, Anders
%A Rognes, Marie E.
%D 2012
%K 76m10-finite-element-methods-in-fluid-mechanics 76d05-incompressible-navier-stokes-equations 65f35-matrix-norms-conditioning-scaling 65n85-fictitious-domain-methods
%T A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem
%U http://arxiv.org/abs/1206.1933
%X We develop a Nitsche fictitious domain method for the Stokes problem starting
from a stabilized Galerkin finite element method with low order elements for
both the velocity and the pressure. By introducing additional penalty terms for
the jumps in the normal velocity and pressure gradients in the vicinity of the
boundary, we show that the method is inf-sup stable. As a consequence, optimal
order a priori error estimates are established. Moreover, the condition number
of the resulting stiffness matrix is shown to be bounded independently of the
location of the boundary. We discuss a general, flexible and freely available
implementation of the method in three spatial dimensions and present numerical
examples supporting the theoretical results.
@misc{citeulike:14289407,
abstract = {{We develop a Nitsche fictitious domain method for the Stokes problem starting
from a stabilized Galerkin finite element method with low order elements for
both the velocity and the pressure. By introducing additional penalty terms for
the jumps in the normal velocity and pressure gradients in the vicinity of the
boundary, we show that the method is inf-sup stable. As a consequence, optimal
order a priori error estimates are established. Moreover, the condition number
of the resulting stiffness matrix is shown to be bounded independently of the
location of the boundary. We discuss a general, flexible and freely available
implementation of the method in three spatial dimensions and present numerical
examples supporting the theoretical results.}},
added-at = {2017-06-29T07:13:07.000+0200},
archiveprefix = {arXiv},
author = {Massing, Andre and Larson, Mats G. and Logg, Anders and Rognes, Marie E.},
biburl = {https://www.bibsonomy.org/bibtex/2fe21b323abcb9de1557dd09cd9cff329/gdmcbain},
citeulike-article-id = {14289407},
citeulike-linkout-0 = {http://arxiv.org/abs/1206.1933},
citeulike-linkout-1 = {http://arxiv.org/pdf/1206.1933},
day = 9,
eprint = {1206.1933},
interhash = {24bd1f566d4c4b143f72338e24091ffc},
intrahash = {fe21b323abcb9de1557dd09cd9cff329},
keywords = {76m10-finite-element-methods-in-fluid-mechanics 76d05-incompressible-navier-stokes-equations 65f35-matrix-norms-conditioning-scaling 65n85-fictitious-domain-methods},
month = jun,
posted-at = {2017-02-28 23:36:02},
priority = {3},
timestamp = {2019-04-17T01:37:00.000+0200},
title = {A Stabilized {N}itsche Fictitious Domain Method for the {S}tokes Problem},
url = {http://arxiv.org/abs/1206.1933},
year = 2012
}