Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



An error estimate of the least squares finite element method for the Stokes problem in three dimensions

Author: Ching Lung Chang
Journal: Math. Comp. 63 (1994), 41-50
MSC: Primary 65N15; Secondary 65N30, 76D07, 76M10
MathSciNet review: 1234425
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we are concerned with the Stokes problem in three dimensions (see recent works of the author and B. N. Jiang for the two-dimensional case). It is a linear system of four PDEs with velocity $ \underline u $ and pressure p as unknowns. With the additional variable $ \underline \omega = {\operatorname{curl}}\underline u $, the second-order problem is reduced to a first-order system. Considering the compatibility condition $ \operatorname{div} \underline \omega = 0$, we have a system with eight first-order equations and seven unknowns. A least squares method is applied to this extended system, and also to the corresponding boundary conditions. The analysis based on works of Agmon, Douglis, and Nirenberg; Wendland; Zienkiewicz, Owen, and Niles; etc. shows that this method is stable in the h-version. For instance, if we choose continuous piecewise polynomials to approximate $ \underline u ,\underline \omega $, and p, this method achieves optimal rates of convergence in the $ {H^1}$-norms.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N15, 65N30, 76D07, 76M10

Retrieve articles in all journals with MSC: 65N15, 65N30, 76D07, 76M10

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society