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 optimal error estimate Optimal Error Estimate of Finite Difference-Streamline Diffusion Methods with Linear Triangular Element for Time-dependent Convection-diffusion Problems 非定常对流扩散问题差分-流线扩散法的线性三角元解的最优误差估计 For the incompressible Stokes problem, we firstly propose mortar element method for Q_1~(rot)/Q_0 element for it, and get the optimal error estimate by proving the inf-sup condition of the discrete saddle point problem. 对不可压缩的Stokes问题,我们首先对它提出Mortar型的Q_1~(rot)/Q_0元方法,通过证明离散鞍点问题的inf-sup条件得到最优误差估计。 Sun and Wheeler[35] also analysed the concentration equation by using the NIPG and SIPG method ,and both methods obtain the optimal error estimate . 在文[35]中,Sun和Wheeler针对渗流问题中的浓度方程给出了NIPG和SIPG方法,两种方法都获得了浓度的最优误差估计。 The Optimal Error Estimate of Streamline Diffusion Finite Element Method for Convection-diffusion Problem 对流扩散问题流线扩散法的最优误差估计 0 restriction on the trial functions, and give their corresponding error analysis and optimal error estimate. 通过对Stokes方程离散格式的构造，我们给出了它们相应的误差分析和最优误差估计。 The convergent property of the V-cycle multigrid method is studied by using intergrid transfer operators and error operators and the optimal error estimate is obtained. 借助于网格转移算子、误差算子等对其V循环多重网格方法的收敛性进行了分析,得到了最优误差估计. At first we derive an optimal error estimate of the resulting approximate solution for two kinds of applicable situations. 我们在文中对两种实用的情况得到了相应的逼近解的最优误差估计。 The aims of this paper are to derive the optimal error estimates of eigenpairs, i.e. the optimal error estimate of eigenvalues, and the new error estimates of velocity, pressure including the L~2 - norm and energy norm, respectively, in which the L~2 - norm estimate of velocity on anisotropic meshes has not ever been seen in the precious literature. 对于Stokes特征值问题本文不仅得到了征值对的最优误差估计即：特征值和流速压力的零模和能量模以及压力的能量模最优误差估计，其中在各向异性网格下对此问题的零模估计尚未见报道。 For Morley's triangular anisotropic nonconforming element we obtains the optimal error estimate of O(h) to variational inequality with curvature obstacle. 对于曲率障碍变分不等式问题的Morley元逼近本文得到了能量模的最优误差估计。 In this paper, by using the orthogonality of Legendre polynomials. A class of product typefive-degree rectsngular elements for solving 2-order problems are constructed,the optimal error estimate is obtained. 利用Legendre多项式的正交性，构造了一类新的乘积型的五节点非协调矩形单元，用它求解二阶椭圆问题，得到了最优误差估计。 This paper presents a kind of local noneonforming element methods to solve the problem of the second order partial differential eguations defined on three dimensional domains with curved boundaries which was solved by finite element method previously and the optimal error estimate is obtained.  本文考虑了三维空间上的一类局部非协调元方法，解决了三维空间光滑区域上的二阶偏微分方程用有限元方法求解的问题，并且得到了最优误差估计。 In this paper, an anisotropic quadrilateral element is presented that can be applied to the displacement obstacle problem. We show that, without the usual regularity condition and quasi-uniform assmption, the same optimal error estimate as that for the traditional finite element method can be obtained. 本文研究了一类可用于位移障碍问题的各向异性任意四边形有限元方法,在不要求通常正则性和拟一致性条件下得到了与传统有限元相同的最优误差估计。 In the previous literature, under the condition of ε≤h~2, the optimal error estimate in L~2 is derived for SDFEM scheme. However, in this paper, we'll improve the condition ε≤h~2 as ε≤h and use a different method to prove the optimal error estimate in L~2 for SDFEM scheme. 原先的文献在ε≤h~2的条件下,得到了L~2-模最优误差估计,而本文则在ε≤h的条件下得到了相同估计。 Secondly,by means of Riesz projection operator and some new approaches,the same optimal error estimate as that for the traditional finite element method can be obtained. 其次,利用Riesz投影算子,通过一些新的技巧和方法,得到与传统有限元相同的最优误差估计. We show that, without the usual regularity assumption, by using some new methods and approaches, we can obtain the same optimal error estimate as that for the traditional finite element method and further extend the application of finite element methods 在区域剖分不要求满足通常的正则性假设下,通过利用新的方法和技巧,得到了与传统有限元相同的最优误差估计结果,从而扩展了有限元的工程应用范围.

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