An optimal order of the multigrid method is given in energy-norm for the nonconforming finite element for solving the biharmonic equation, by using the nodal interpolation operator as the transfer operator between grids.
An optimal order of the multigrid method is given in energy-norm for the nonconforming finite element for solving the biharmonic equation, by using the nodal interpolation operator as the transfer operator between grids.
A comparison theorem concerning the regularity of Brikhoff interpolation is given. As an application of this theorem the regularity of (0,1,...,p - 1, p + 1,...,M - 1, q) interpolation (0 < p < M less-than-or-eq...
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A comparison theorem concerning the regularity of Brikhoff interpolation is given. As an application of this theorem the regularity of (0,1,...,p - 1, p + 1,...,M - 1, q) interpolation (0 < p < M less-than-or-equal-to q) is characterized.
A method for construction of a preconditioner for the capacitance matrix on the interface is described. The preconditioner is determined by a subdomain covering the interface, and the condition number of the precondit...
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A method for construction of a preconditioner for the capacitance matrix on the interface is described. The preconditioner is determined by a subdomain covering the interface, and the condition number of the preconditioned matrix is dependent on the width of the covering subdomain and independent of the discrete mesh size and discontinuity of the coefficients of the differential operator. Some applications of our theory are presented at last.
A fast algorithm for evaluating and displaying bivariate splines in a three direction is presented based on two-level transfomation of the corresponding B-splines. The efficiency has been shown by experiments of surfa...
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A fast algorithm for evaluating and displaying bivariate splines in a three direction is presented based on two-level transfomation of the corresponding B-splines. The efficiency has been shown by experiments of surface modelling design[5].
A necessary and sufficient condition of regularity of (0,1,…, m - 2, m) interpo-lation on the zeros of the Laguerre polynomials Ln(α) (x) (α≥ -1) in a manageable form is established. Meanwhile, the explicit repres...
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A necessary and sufficient condition of regularity of (0,1,…, m - 2, m) interpo-lation on the zeros of the Laguerre polynomials Ln(α) (x) (α≥ -1) in a manageable form is established. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given. Moreover, it is shown that, if the problem of (0,1,…, m - 2, TO) interpolation has an infinity of solutions, then the general form of the solutions is f0(x) + Cf1(x) with an arbitrary constant C.
In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see add...
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In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see additive extrapolation method before. This new method has a great advantage over additive extrapolation method because it keeps group property. If this method is used to construct higher order schemes from lower symplectic schemes, the higher order ones are also symplectic. First we introduce the concept of adjoint methods and some of their properties. We show that there is a self-adjoint scheme corresponding to every method. With this self-adjoint scheme of lower order, we can construct higher order schemes by multiplicative extrapolation method, which can be used to construct even much higher order schemes. Obviously this constructing process can be continued to get methods of arbitrary even order.
A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; t...
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A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is 0(1 + log H/h), where H and h are mesh sizes of the unrefined and local refined triangulations respectively.
In this paper, we present a new semi-discrete difference scheme for the KdV equation, which possesses the first four nearconserved quatities. The scheme is better than the past one given in [4], because its solution ...
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In this paper, we present a new semi-discrete difference scheme for the KdV equation, which possesses the first four nearconserved quatities. The scheme is better than the past one given in [4], because its solution has a more superior estimation. The convergence and the stability of the new scheme are proved
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