Least-squares finite element methods for the elasticity problem

Suh Yuh Yang, Jinn Liang Liu

研究成果: 雜誌貢獻期刊論文同行評審

9 引文 斯高帕斯(Scopus)


A new first-order system formulation for the linear elasticity problem in displacement-stress form is proposed. The formulation is derived by introducing additional variables of derivatives of the displacements, whose combinations represent the usual stresses. Standard and weighted least-squares finite element methods are then applied to this extended system. These methods offer certain advantages such as that they need not satisfy the inf-sup condition which is required in the mixed finite element formulation, that a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, that the resulting algebraic systems are symmetric and positive definite, and that accurate approximations of the displacements and the stresses can be obtained simultaneously. With displacement 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 Poisson ratios are given to demonstrate the theoretical error estimates.

頁(從 - 到)39-60
期刊Journal of Computational and Applied Mathematics
出版狀態已出版 - 18 12月 1997


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