標題: Least-squares finite element methods for the elasticity problem
作者: Yang, SY
Liu, JL
應用數學系
Department of Applied Mathematics
關鍵字: elasticity;Poisson ratios;elliptic systems;least squares;finite elements;convergence;error estimates
公開日期: 18-十二月-1997
摘要: 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 H-1-norm and in the L-2-norm for all the unknowns. Numerical experiments with various Poisson ratios are given to demonstrate the theoretical error estimates.
URI: http://hdl.handle.net/11536/140
ISSN: 0377-0427
期刊: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume: 87
Issue: 1
起始頁: 39
結束頁: 60
顯示於類別:期刊論文


文件中的檔案:

  1. 000071396700004.pdf