NDLI: First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Cai, Z. Lee, C. O. Manteuffel, T. A. McCormick, S. F.
Copyright Year	2000
Abstract	First-order system least squares (FOSLS) was developed in [ SIAM J. Numer. Anal., 34 (1997), pp. 1727--1741; SIAM J. Numer. Anal., 35 (1998), pp. 320--335] for Stokes and elasticity equations. Several new results for these methods are obtained here. First, the inverse-norm FOSLS scheme that was introduced but not analyzed in [ SIAM J. Numer. Anal., 34 (1997), pp. 1727--1741] is shown to be continuous and coercive in the L2 norm. This result is shown to hold for pure displacement or pure traction boundary conditions in two or three dimensions, and for mixed boundary conditions in two dimensions. Next, the FOSLS schemes developed in [ SIAM J. Numer. Anal., 35 (1998), pp. 320--335] are applied to the pure displacement problem in planar and spatial linear elasticity byeliminating the pressure variable in the FOSLS formulations of [SIAM J. Numer. Anal., 34 (1997), pp. 1727--1741]. The idea of two-dimensional variable rotation is then extended to three dimensions to make the intervariable coupling subdominant (uniformly so in the Poisson ratio for elasticity). This decoupling ensures optimal (uniform) performance of finite element discretization and multigrid solution methods. It also allows special treatment of the new trace variable, which corresponds to the divergence of velocity in the case of Stokes, so that conservation can be easily imposed, for example. Numerical results for various boundary value problems of planar linear elasticity are studied in a companion paper [SIAM J. Sci. Comput., 21 (2000), pp. 1706--1727].
Starting Page	1728
Ending Page	1739
Page Count	12
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827598338652
e-ISSN	10957197
Issue Number	5
Volume Number	21
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Stokes Other matrix algorithms Iterative methods for linear systems least squares elasticity multigrid
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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