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optimal error estimates
    Stability and convergence of the totally discrete finite element method for a class of second order nonlinear coupled equations arising in the thermoelastic theory are discussed, and the optimal error estimates between the exact solution and the FEM solutions in H~1, L~2, L~∞ norm are obtained.
    本文讨论出现在热弹性理论中一类非线性双曲—抛物耦合方程全离散有限元方法的收敛性和稳定性,并给出了真解和有限元解在L~2,H~1,L~∞意义下的最优误差估计。 该类问题的半离散方法见[1],[2]。
    HFEM (Homotopy Finite Element Method) is used to investigate a class of arch beam models. Optimal error estimates are obtained and some superconvergence results are established.
    用同伦有限元法研究了一类拱梁问题,并得到了最优误差估计和超收敛结果.与古典位移变分方法相比,此结果对位移的误差估计是最优的;
    Under the Ostrowski-Kantorovich condi- tions a successful existence-convergence theorem of iteration procedures for 0≤μ≤2 is estab- lished. Meanwhile,the optimal error estimates for 0≤μ≤2 are obtained.
    在 Ostrowski-Kantorovich 条件下建立对0≤μ≤2的收敛性定理,且得到对0≤μ≤2的最优误差估计.
    The optimal error estimates in H's is proved.
    利用椭圆投影及其误差估计,建立了计算格式在H模意义下的最优误差估计
    In this paper we give the optimal error estimates of Petrov-Galerkin finite element (PGFE) methods for the initial-value problem of nonlinear Volterra integro-differential equations.
    在本文中 ,对于非线性维他里积分微分方程的初值问题 ,我们给出了PGFE方法的最优误差估计 .
    Moreover, we apply the CNR element to the nearly incompressible planar elasticity problem, and obtain uniformly optimal error estimates in both energy and L2 norm, which is independent of the Lame constant λ.
    同时应用CNR元求解几乎不可压平面弹性问题,在能量范数与L~2范数意义下得到了与Lame数λ无关的最优误差估计
    In Chapter two, we consider the finite volume element Methods for nonlinear parabolic problemsOptimal order error estimates in the H1, L2norms and W1,∞ almost optimal error estimates in L∞ are demonstrated. Moreover superconvergence in the error between the approximate solution and the generalized elliptic projection of the exact solution is also shown.
    第二章考虑非线性抛物方程的初值问题的体积有限元法,并证明了H~1,L_2和W~(1,∞)误差估计以及L_∞最优误差估计,而且还得到了近似解和真解的广义椭圆投影间的超收敛估计。
    In Chapter three, we consider the finite volume element Mstheods for nonlinear hyperbolic problemsOn the basic of the chapter three , Optimal order error estimates in the H1, L2norms and W1,∞ almost optimal error estimates in L∞ are also demonstrated. Moreover super-convergence in the error between the approximate solution and the generalized elliptic projection of the exact solution is also shown.
    第三章考虑非线性双曲方程的初值问题的体积有限元法。 在第二章的基础上也得到了H~1,L_2和W~(1,∞)误差估计以及L_∞最优误差估计和近似解和真解的广义椭圆投影间的超收敛估计。
    We first consider the nonoconforming finite element approximation for the second order variational obstacle problem. By means of the novel techniques, the optimal error estimates are obtained, which are as same as the results of the conventional finite element element methods.
    首先研究二阶变分不等式问题的非协调有限元逼近,通过运用新的方法和技巧,得到了与传统有限元方法相同的最优误差估计
    At the same time, by introducing special novel approaches, the optimal error estimates of energy norm and L~2- norm are obtained, which are as same as that of the traditional finite element methods. Thus we get rid of the restrictions of the regularity assumption and quasi-uniform assumption required on the meshes in the conventional finite element methods analysis, and extend the application scope of nonconforming finite elements.
    通过引入新的特殊技巧和方法得到了能量范数及L~2-范数的最优误差估计,从而克服了传统有限元方法对网格剖分要求满足正则性假设或拟一致假设等严重缺陷,拓宽了非协调有限元的应用范围。
    At the same time, by using the Rieszprojection, the optimal error estimates in energy norm and L~2-norm ofare obtained.
    利用该元的某些特殊性质,结合变网格思想,通过Riesz投影技巧,导出了全离散的变网格格式,给出了各向异性条件下能量模和L~2-模的最优误差估计
    First, we applied these finite element approximations to hyperbolic intergrodifFerential equations with semidiscretization on anisotropic meshes, the same optimal error estimates and superclose properties as the traditional methods are derived.
    首先讨论了双曲积分微分方程在半离散格式下的一类各向异性非协调有限元逼近,得到了与传统有限元方法相同的最优误差估计和超逼近性质。
    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。
    By using some novel approaches and techniques, the same optimal error estimates are obtained as the traditional methods.
    并且通过采用一系列新的技巧和方法,得到了与传统有限元方法完全相同的最优误差估计
    The optimal error estimates are given.
    同时给出了最优误差估计
    The merits of characteristic finite element methods are preserved and the optimal error estimates,which cold not be got by using standard finite element method,are obtained for the scheme. At the same time,piecewise finite element space can be used in this method.
    该法不仅避免了用混合元法求解压力方程带来的困难 ,而且保持了特征有限元方法的优点 ,得到用标准有限元方法求解压力方程著不能得到的最优误差估计
    Taking Bergan's element for example, the approximation method of strong discontinuous finite elements for fourth order eigenvalue problems is discussed, and the optimal error estimates are obtained. Therefore the results obtained before are improved.
    以 Bergan元为例 ,讨论了四阶特征值问题强间断有限元的逼近方法 ,得到了最优误差估计 ,改善或弥补了以往文献的结果和不足 .
    Using the method of analysing Specht element, the application of nonconforming arbitrary quadrilateral element to the unilateral problem is studied, and the convergence analysis and optimal error estimates are given.
    利用分析 Specht元的技巧 ,研究将非协调任意四边形单元应用于单侧问题 ,给出了相应的收敛性分析和最优误差估计 .
    According to the alternation method,after transforming change these coupling nonlinear equations into two separate noncoupling equations. Finally,we use initial value to obtain that result is the optimal error estimates in the L 2-norm.
    根据交替法的思想 ,将这一耦合非线性方程组变成两个独立的非耦合的方程 ,最后利用初值得出在L2 范数下的最优误差估计式 .
    A general Tikhonov regularization has been given by Schroter T and Tautenhahn U, and the optimal error estimates have been considered.
    Schrroter T 和Tautenhahn U给出了一类广义Tikhonov正则化方法并重点讨论了它的最优误差估计, 但却未能对该方法的饱和效应进行研究.
 

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