Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Analysis of least squares finite element methods for the Stokes equations

Authors: Pavel B. Bochev and Max D. Gunzburger
Journal: Math. Comp. 63 (1994), 479-506
MSC: Primary 76M10; Secondary 65N30, 76D07
MathSciNet review: 1257573
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the application of least squares principles to the approximate solution of the Stokes equations cast into a first-order velocity-vorticity-pressure system. Among the most attractive features of the resulting methods are that the choice of approximating spaces is not subject to the LBB condition and a single continuous piecewise polynomial space can be used for the approximation of all unknowns, that the resulting discretized problems involve only symmetric, positive definite systems of algebraic equations, that no artificial boundary conditions for the vorticity need be devised, and that accurate approximations are obtained for all variables, including the vorticity. Here we study two classes of least squares methods for the velocity-vorticity-pressure equations. The first one uses norms prescribed by the a priori estimates of Agmon, Douglis, and Nirenberg and can be analyzed in a completely standard manner. However, conforming discretizations of these methods require $ {C^1}$ continuity of the finite element spaces, thus negating the advantages of the velocity-vorticity-pressure formulation. The second class uses weighted $ {L^2}$-norms of the residuals to circumvent this flaw. For properly chosen mesh-dependent weights, it is shown that the approximations to the solutions of the Stokes equations are of optimal order. The results of some computational experiments are also provided; these illustrate, among other things, the necessity of introducing the weights.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 76M10, 65N30, 76D07

Retrieve articles in all journals with MSC: 76M10, 65N30, 76D07

Additional Information

PII: S 0025-5718(1994)1257573-4
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia