Analysis of least squares finite element methods for a parameter-dependent first-order system*
作者:
Suh-Yuh Yang,
Jinn-Liang Liu,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1998)
卷期:
Volume 19,
issue 1-2
页码: 191-213
ISSN:0163-0563
年代: 1998
DOI:10.1080/01630569808816823
出版商: Marcel Dekker, Inc.
关键词: least squares;finite elements;convergence;error estimates;elasticity equations;Poisson's ratios;Stokes equations;AMS(MOS) Subject Classifications. 65N30;AMS(MOS) Subject Classifications.73V05;AMS(MOS) Subject Classifications.76M10
数据来源: Taylor
摘要:
A parameter-dependent first-order system arising from elasticity problems is introduced. The system corresponds to the 2D isotropic elasticity equations under a stress-pressure-displacement formulation in which the nonnegative parameter measures the material compressibility for the elastic body. Standard and weighted least squares finite element methods are applied to this system, and analyses for different values of the parameter are performed in a unified manner. The methods offer certain advantages such as they need not satisfy the Babuŝka-Brezzi condition, a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, the resulting algebraic system is symmetric and positive definite, accurate approximations of all the unknowns can be obtained simultaneously, and, especially, computational results do not exhibit any significant numerical locking as the parameter tends to zero which corresponds to the incompressible elasticity problem (or equivalently, the Stokes problem). With suitable boundary conditions, it is shown that both methods achieve optimal rates of convergence in the H1-norm and in the L2-norm for all the unknowns. Numerical experiments with various values of the parameter are given to demonstrate the theoretical estimates.
点击下载:
PDF (1956KB)
返 回