International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 699-714

Stable finite element methods for the Stokes problem

Yongdeok Kim and Sungyun Lee

Department of Mathematics, KAIST, Taejon 305-701, Korea

Received 11 March 1999

Copyright © 2000 Yongdeok Kim and Sungyun Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The mixed finite element scheme of the Stokes problem with pressure stabilization is analyzed for the cross-grid PkPk1elements, k1, using discontinuous pressures. The Pk+Pk1 elements are also analyzed. We prove the stability of the scheme using the macroelement technique. The order of convergence follows from the standard theory of mixed methods. The macroelement technique can also be applicable to the stability analysis for some higher order methods using continuous pressures such as Taylor-Hood methods, cross-grid methods, or iso-grid methods.