%0 Journal Article %1 arnold1984stable %A Arnold, D. N. %A Brezzi, F. %A Fortin, M. %D 1984 %I Springer %J Calcolo %K 35q30-navier-stokes-equations 76d05-incompressible-navier-stokes-equations 76d07-stokes-and-related-oseen-etc-flows 76m10-finite-element-methods-in-fluid-mechanics %N 4 %P 337--344 %R 10.1007/bf02576171 %T A Stable Finite Element for the Stokes Equations %U https://link.springer.com/article/10.1007%2FBF02576171 %V 21 %X We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we relate this element to families of higer order elements and to the popular Taylor-Hood element.

@article{arnold1984stable, abstract = {{We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we relate this element to families of higer order elements and to the popular Taylor-Hood element.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Arnold, D. N. and Brezzi, F. and Fortin, M.}, biburl = {https://www.bibsonomy.org/bibtex/287b8aa9e7ab1f60b3d64bd3b6c9bed36/gdmcbain}, citeulike-article-id = {2734896}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/bf02576171}, citeulike-linkout-1 = {http://www.springerlink.com/content/a54722r712511871}, citeulike-linkout-2 = {http://link.springer.com/article/10.1007/BF02576171}, day = 1, doi = {10.1007/bf02576171}, interhash = {ae75ecd2ef91461caf834efc8caa754d}, intrahash = {87b8aa9e7ab1f60b3d64bd3b6c9bed36}, issn = {0008-0624}, journal = {Calcolo}, keywords = {35q30-navier-stokes-equations 76d05-incompressible-navier-stokes-equations 76d07-stokes-and-related-oseen-etc-flows 76m10-finite-element-methods-in-fluid-mechanics}, month = dec, number = 4, pages = {337--344}, posted-at = {2016-06-09 01:43:40}, priority = {4}, publisher = {Springer}, timestamp = {2020-07-10T06:59:59.000+0200}, title = {A Stable Finite Element for the {S}tokes Equations}, url = {https://link.springer.com/article/10.1007%2FBF02576171}, volume = 21, year = 1984 }