International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 699-714
doi:10.1155/S0161171200002908
Stable finite element methods for the Stokes problem
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.
Abstract
The mixed finite element scheme of the Stokes problem with
pressure 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 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.