%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 }