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

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

Received 11 March 1999

Copyright © 2000 Hindawi Publishing Corporation. 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 withpressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using themacroelement technique. The order of convergence follows from the standardtheory of mixed methods. The macroelement technique can also be applicableto the stability analysis for some higher order methods using continuouspressures such as Taylor-Hood methods, cross-grid methods, or iso-gridmethods.

Author: Yongdeok Kim and Sungyun Lee



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