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🏛️國立陽明交通大學機構典藏

Author: search.filters.author.Yang, SYHas files: No

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    Analysis of least squares finite element methods for a parameter-dependent first-order system
    (1998-01-01)
    Yang, SY
    ;
    Liu, JL
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    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 Babuska-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 H-1-norm and in the L-2-norm for all the unknowns. Numerical experiments with various values of the parameter are given to demonstrate the theoretical estimates.
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    Item type:Item,
    A least-squares finite element method for incompressible flow in stress-velocity-pressure version
    (1995-12-01)
    Chang, CL
    ;
    Yang, SY
    ;
    Hsu, CH
    ;
    交大名義發表
    ;
    National Chiao Tung University
    In this paper we are concerned with the incompressible flow in 2-D. Introducing additional variables of derivatives of velocity, which are called stresses here, the second-order dynamic equations are reduced into a first-order system with variables of stress, velocity and pressure. Combining the compatibility condition and the divergence free condition, we have a system with six first-order equations and six unknowns. Least-squares method is performed over this extended system. The analysis shows that this method achieves optimal rates of convergence in the H-1-norm as the h approaches to zero. Numerical experiences are also available.
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    Item type:Item,
    Least-squares finite element methods for the elasticity problem
    (1997-12-18)
    Yang, SY
    ;
    Liu, JL
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    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.
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    Item type:Item,
    Stability investigation of single-wafer process by using a spin etcher
    (2003-07-01)
    Kang, TK
    ;
    Wang, CC
    ;
    Tsui, BY
    ;
    Yang, WL
    ;
    Chien, FT
    Etch rate instability was found in a spin etcher. When chemical was pumped to the spin etcher, the flow rate became unstable; possibly resulting in a chemical deficiency due to low mass transport at the wafer edge. Consequently, the etch rate and etch uniformity are unstable. The detailed etch mechanism has been investigated and the mass transport deficiency can be avoided. Less than 2% of etch nonuniformity and a stable process can be achieved by achieving a stable flow rate and control of the surface reaction over the whole wafer in spin etching. (C) 2003 The Electrochemical Society.
  • Thumbnail Image
    Item type:Item,
    A least-squares finite element method for incompressible flow in stress-velocity-pressure version
    (1995-12-01)
    Chang, CL
    ;
    Yang, SY
    ;
    Hsu, CH
    ;
    交大名義發表
    ;
    National Chiao Tung University
    In this paper we are concerned with the incompressible flow in 2-D. Introducing additional variables of derivatives of velocity, which are called stresses here, the second-order dynamic equations are reduced into a first-order system with variables of stress, velocity and pressure. Combining the compatibility condition and the divergence free condition, we have a system with six first-order equations and six unknowns. Least-squares method is performed over this extended system. The analysis shows that this method achieves optimal rates of convergence in the H-1-norm as the h approaches to zero. Numerical experiences are also available.