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本文研究了一类椭圆型奇异摄动问题.利用Bakhvalov-Shishkin网格上的差分方法,获得了数值解一致一阶收敛于真解的结果. 相似文献
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数值积分对特征值有限元外推的影响 总被引:1,自引:0,他引:1
杨一都 《应用数学与计算数学学报》1989,3(1):48-54
§1.引言在分片一致三角形剖分下,用线性有限元法解特征值问题求得近似特征值λ、λ~(h/2).[1]证明了对λ~h.λ~(h/2)作外推可提高收敛阶: 相似文献
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小参数常微分方程守恒型差分格式的一致收敛性 总被引:1,自引:0,他引:1
本文考虑自共轭常微分方程奇异摄动边值问题,构造一族带拟合因子的差分格式,给出差分格式解一致收敛于微分方程解的充分条件,由此提出几个具体格式,在条件较弱的情况下,给出较高的一致收敛阶。 相似文献
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具有零阶退化方程的二阶双曲型方程奇异摄动问题的一致差分格式 总被引:1,自引:1,他引:0
本文讨论了一个二阶双曲型奇异摄动问题,它的一阶导数项含有小参数ε.首先给出该问题解的能量估计及渐近解的余项估计,然后在均匀网格上构造了一个指数型拟合差分格式,最后证明了差分解在离散的能量范数意义下一致收敛于问题的精确解. 相似文献
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利用双线性元的积分恒等式,给出了二维非定常对流占优扩散方程的特征线有限元解和真解的一致误差估计,并利用插值后处理算子给出了有限元解梯度的一致超收敛估计,即上述误差与ε无关,而仅与右端f和初值u_0有关. 相似文献
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利用三角形线性元的积分恒等式,给出了二维非定常对流占优扩散方程的特征线有限元解和真解的一致最优估计,并利用插值后处理算子,得到了有限元解梯度的一致超收敛估计,即只与初值和右端项有关,而与ε无关. 相似文献
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针对一类非线性色散耗散波动方程研究了双线性元逼近.基于该元的高精度分析和插值后处理技巧,对于半离散格式,在精确解的合理正则性假设下得到了H~11模意义下最优误差估计及超逼近性和超收敛结果.同时,通过构造一个新的外推格式,导出了具有三阶精度的外推解.最后,建立了一个全离散逼近格式及研究其解的超逼近性. 相似文献
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本文对守恒型自共轭奇异摄动常微分方程,利用El-Mistikawy和Werle[1]的思想构造一个差分格式,并证明该格式为关于ε一致收敛的二阶格式. 相似文献
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We investigate the limit functions of iterates of a functionbelonging to a convergence group or of a uniformly quasiregularmapping. We show that it is not possible for a subsequence ofiterates to tend to a non-constant limit function, and for anothersubsequence of iterates to tend to a constant limit function.It follows that the closure of the stabiliser of a Siegel domainfor a uniformly quasiregular mapping is a compact abelian Liegroup, which we further conjecture to be infinite. This resultconcerning possible limits of convergent subsequences of iteratesfor holomorphic rational functions on the Riemann sphere isknown, and the only known method of proof involves universalcovering surfaces and Möbius groups. Hence, our methodyields a new and perhaps more elementary proof also in thatcase. 相似文献
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Li Wang Yongke WU Xiaoping Xie 《Numerical Methods for Partial Differential Equations》2013,29(3):721-737
In this article, we consider rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non‐ C0 rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a C0 extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical experiments to confirm the theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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We consider a singular perturbation problem which describes 2D Darcy-Stokes flow.An H(div)-conforming rectangular element,DS-R14,is proposed and analyzed frst.This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant.We then simplify this element to get another H(div)-conforming rectangular element,DS-R12,which has 12 degrees of freedom for velocity.The uniform convergence is also obtained for this element.Finally,we construct a de Rham complex corresponding to DS-R12 element. 相似文献
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We shall introduce the notion of uniformly classical primary submodule that generalizes the concept of uniformly primary ideal as given by J. A. Cox and A. J. Hetzel. We also advance the companion concepts of fully uniformly classical primary module and uniformly primary compatible module. Along these lines, we present a characterization of Noetherian rings R for which every R-module is fully uniformly classical primary and we present a characterization of rings R for which every finitely generated R-module is uniformly primary compatible. Results illustrating connections among the notions of uniformly classical primary submodule, uniformly primary ideal, and uniformly primary submodule as given by R. Ebrahimi-Atani and S. Ebrahimi-Atani are also provided. 相似文献
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Hongru Chen Shaochun Chen Liuchao Xiao 《Numerical Methods for Partial Differential Equations》2014,30(6):1785-1796
In this article, we introduce a C 0‐nonconforming triangular prism element for the fourth‐order elliptic singular perturbation problem in three dimensions by using the bubble functions. The element is proved to be convergent in the energy norm uniformly with respect to the perturbation parameter. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1785–1796, 2014 相似文献
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Wee -Kee Tang 《Archiv der Mathematik》1997,68(1):55-59
We present a construction of uniformly smooth norms from uniformly smooth bumb functions without making use of the Implicit Function Theorem. 相似文献
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In this paper, we construct a kind of novel finite difference (NFD) method for solving singularly perturbed reaction–diffusion problems. Different from directly truncating the high‐order derivative terms of the Taylor's series in the traditional finite difference method, we rearrange the Taylor's expansion in a more elaborate way based on the original equation to develop the NFD scheme for 1D problems. It is proved that this approach not only can highly improve the calculation accuracy but also is uniformly convergent. Then, applying alternating direction implicit technique, the newly deduced schemes are extended to 2D equations, and the uniform error estimation based on Shishkin mesh is derived, too. Finally, numerical experiments are presented to verify the high computational accuracy and theoretical prediction. 相似文献