%0 Journal Article %1 citeulike:12939631 %A Bernardi, Christine %A Hecht, Frédéric %A Nouri, Fatma Z. %D 2010 %I Oxford University Press %J IMA Journal of Numerical Analysis %K 76s05-flows-in-porous-media 76m10-finite-element-methods-in-fluid-mechanics 76d07-stokes-and-related-oseen-etc-flows %N 1 %P 61--93 %R 10.1093/imanum/drn054 %T A new finite-element discretization of the Stokes problem coupled with the Darcy equations %U http://dx.doi.org/10.1093/imanum/drn054 %V 30 %X The flow in a rigid porous medium with a crack is usually modelled by the Darcy equations coupled with the Stokes problem. We first propose a new variational formulation of the Stokes system, where the unknowns are the vorticity, the velocity and the pressure, and describe the corresponding finite-element discretization. We extend this discretization to the case where the Darcy and the Stokes equations are coupled and prove optimal a priori and a posteriori error estimates. We conclude with some numerical experiments.

@article{citeulike:12939631, abstract = {{The flow in a rigid porous medium with a crack is usually modelled by the Darcy equations coupled with the Stokes problem. We first propose a new variational formulation of the Stokes system, where the unknowns are the vorticity, the velocity and the pressure, and describe the corresponding finite-element discretization. We extend this discretization to the case where the Darcy and the Stokes equations are coupled and prove optimal a priori and a posteriori error estimates. We conclude with some numerical experiments.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Bernardi, Christine and Hecht, Fr\'{e}d\'{e}ric and Nouri, Fatma Z.}, biburl = {https://www.bibsonomy.org/bibtex/260fe5c7e79d51b3a3a8ccb0abb840194/gdmcbain}, citeulike-article-id = {12939631}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/imanum/drn054}, citeulike-linkout-1 = {http://imajna.oxfordjournals.org/content/30/1/61.abstract}, citeulike-linkout-2 = {http://imajna.oxfordjournals.org/content/30/1/61.full.pdf}, comment = {(private-note)circulated by jon.sauer 2014-01-25}, day = 01, doi = {10.1093/imanum/drn054}, interhash = {44085d69c5639fc1cd42301c602839a3}, intrahash = {60fe5c7e79d51b3a3a8ccb0abb840194}, issn = {1464-3642}, journal = {IMA Journal of Numerical Analysis}, keywords = {76s05-flows-in-porous-media 76m10-finite-element-methods-in-fluid-mechanics 76d07-stokes-and-related-oseen-etc-flows}, month = jan, number = 1, pages = {61--93}, posted-at = {2014-01-27 22:06:53}, priority = {2}, publisher = {Oxford University Press}, timestamp = {2019-02-28T23:44:48.000+0100}, title = {{A new finite-element discretization of the Stokes problem coupled with the Darcy equations}}, url = {http://dx.doi.org/10.1093/imanum/drn054}, volume = 30, year = 2010 }