In this paper, a nonlinear Galerkin (semi-discrete) mixed element method for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approxima...
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In this paper, a nonlinear Galerkin (semi-discrete) mixed element method for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity,defined respectively on a coarse grid with grid size H and another fine grid with grid size h << H, a finite element space Mh for the approximation of the pressuxe and two finite element spaces WH and Wh for the approximation of the temperature,also defined respectively on the coarse grid with grid size H and another fine grid with grid size h << H. Both of the non linearity and time dependence are treated only in the coarse space. We have proved that the error between the nonlinear Galerkin mixed element solution and standard Galerkin mixed element solutionis of the order of Hm+1(m>1), all in velocity (H1(Ω)2 norm), pressure (L2(Ω)norm) and temperature (H1 (Ω) norm).
In this paper, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is b...
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In this paper, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity, defined respectively on a coarse grid with grids size H and another fine grid with grid size h<< H, a finite element space Mh for the approximation of the pressure and two finite element spaces AH and Wh, for the approximation of the temperature,also defined respectivply on the coarse grid with grid size H and another fine grid with grid size h. The existence and the convergence of the fully discrete mixed element solution are shown. The scheme consists in using standard backward one step Euler-Galerkin fully discrete format at first L0 steps (L0 2) on fine grid with grid size h, but using nonlinear Galerkin mixed element method of backward one step Euler-Galerkin fully discrete format through L0 + 1 step to end step. We have proved that the fully discrete nonlinear Galerkin mixed element procedure with respect to the coarse grid spaces with grid size H holds superconvergence.
Based on the two-scale asymptotic analysis method for elastic structures of composite materials formed by entirely basic configurations, the finite element formulation and its error estimates are presented in this pap...
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Based on the two-scale asymptotic analysis method for elastic structures of composite materials formed by entirely basic configurations, the finite element formulation and its error estimates are presented in this paper. Meanwhile, the approximate formulas of Du are also set up.
In this paper, we present a simplified third-order weighted ENO finite volume method on unstructured triangular mesh. The third-order TVD Runge-Kutta time diswcretization is used. A weighted quadratic reconstruction i...
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In this paper, we present a simplified third-order weighted ENO finite volume method on unstructured triangular mesh. The third-order TVD Runge-Kutta time diswcretization is used. A weighted quadratic reconstruction is constructed on every triangular mesh. Preliminary encouraging numerical experiment is given.
In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m s...
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In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.
In the exact nonparametric illference, we frequelltly need the enumeration of all contingency tables with the same marginal totals. A qualltum jump toward a more rapid method took place with the publication of the net...
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In the exact nonparametric illference, we frequelltly need the enumeration of all contingency tables with the same marginal totals. A qualltum jump toward a more rapid method took place with the publication of the network approach of Mehta et al.[1-3]. It circumvents the need to explicitly enumerate each table and considerably extends the bounds of computational feasibility relative to the direct enumeration. In this paper) the present authors suggest another algorithm of implicit enumeration of all tables. First, a contingency table (T × c table or stratified 2×c table) is regarded as a number with several digits, and all contingency tables with the same marginal totals are regarded as a number sequence. A rule is then intyoduced to generate the sequence and to leap some subsequences which are useless for computing the probability values. The leaping subsequence aIgorithm proposed is more efficient than the network algorithm. Especially, when-the permutation distribution is required, our algorithm may run tens times faster than StatXact.[4]
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