Browsing by Author "LIU, JL"

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A FINITE-DIFFERENCE METHOD FOR SYMMETRICAL POSITIVE DIFFERENTIAL-EQUATIONS
(1994-01-01)
LIU, JL
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交大名義發表
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應用數學系
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National Chiao Tung University
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Department of Applied Mathematics
A finite difference method is developed for solving symmetric positive differential equations in the sense of Friedrichs. The method is applicable to partial differential equations of mixed type with more general boundary conditions. The method is shown to have a convergence rate of O(h(1/2)), h being the size of mesh grid. Some numerical results are presented for a model problem of forward-backward heat equations.
A-POSTERIORI FINITE-ELEMENT ERROR ESTIMATORS FOR INDEFINITE ELLIPTIC BOUNDARY-VALUE-PROBLEMS
(1994)
LIU, JL
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RHEINBOLDT, WC
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應用數學系
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Department of Applied Mathematics
A general construction technique is presented for a posteriori error estimators of finite element solutions of elliptic boundary value problems that satisfy a Garding inequality. The estimators are obtained by an element-by-element solution of 'weak residual' problems with or without considering element boundary residuals. There is no order restriction on the finite element spaces used for the approximate solution or the error estimation; that is, the design of the estimators is applicable in connection with either one of the h-, p-, or hp- formulations of the finite element method. Under suitable assumptions it is shown that the estimators are bounded by constant multiples of the true error in a suitable norm. Some numerical results are given to demonstrate the effectiveness and efficiency of the approach.
WEAK RESIDUAL ERROR-ESTIMATES FOR SYMMETRICAL POSITIVE SYSTEMS
(1993)
LIU, JL
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應用數學系
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Department of Applied Mathematics
A weak-residual type error estimation for finite element solutions of symmetric positive systems in the sense of Friedrichs' is proposed. The estimator calculates a residual error interior to an element with no consideration of boundary residual, thus allowing for element-by-element computations. The estimator is proved to be bounded by the exact error in suitably defined norm with multiple constants. A priori and a posteriori numerical estimates are presented for a forward-backward heat equation model problem.