共查询到17条相似文献,搜索用时 78 毫秒
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《数学的实践与认识》2015,(22)
对二阶椭圆问题构造了一个非常规各向异性Hermite型矩形单元.并基于泡函数对其构造了一种简化的稳定化混合元格式.同时给出了格式的收敛性分析和后验误差估计. 相似文献
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可压缩Navier-Stokes方程的压力梯度局部投影间断有限元法 总被引:1,自引:0,他引:1
将压力梯度投影与间断有限元法相结合,对可压缩线性化N-S方程提出了一种稳定化间断有限元格式.证明了此格式在速度和压力有限元空间无需满足B-B型条件的情况下,解的存在性和唯一性,以及相应的误差估计. 相似文献
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本文将局部投影稳定化(LPS)方法和连续时空有限元方法相结合研究对流扩散反应方程,给出稳定化连续时空有限元离散格式.与传统的时空有限元研究思路不同,时间方向利用Lagrange插值多项式,解耦时间和空间变量,降低时空有限元解的维数,具有减少计算量和简化理论分析的优点.通过引入Legendre多项式给出了有限元解的稳定性分析,进一步引进Lobatto多项式证明了有限元解的全局L∞(L2)和局部L2(Jn;LPS)范数误差估计.最后给出数值算例验证理论分析的正确性,以及稳定化格式的可行性和有效性. 相似文献
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非定常Stokes方程一种基于POD方法的简化有限差分格式 总被引:1,自引:1,他引:0
特征正交分解(proper orthogonal decomposition,简记为POD)方法是一种可对偏微分方程的物理模型(如流体流动)做简化的技术.这种方法已经成功地用于对复杂系统模型降阶.推广应用POD方法,将POD方法应用于具有实际应用背景的非定常Stokes方程经典的有限差分格式,建立一种维数较低而精度足够高的简化差分格式,并给出简化差分格式解与经典差分格式解的误差估计.数值例子说明数值计算结果与理论结果相吻合.进一步表明基于POD方法的简化差分格式对求解非定常Stokes方程数值解是可行和有效的. 相似文献
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Stokes方程的稳定化间断有限元法 总被引:5,自引:2,他引:3
本文对定常的Stokes方程提出了一种新的间断有限元法,通过对通常的间断Galerkin有限元法应用稳定化思想,建立了一个相容的稳定间断有限元格式,对速度和压力的任意分片多项式空间Pl(K),Pm(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L2 范数的最优误差估计. 相似文献
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特征值问题混合有限元法的一个误差估计 总被引:3,自引:0,他引:3
设(λh,σh,uh)是一个混合有限元特征对.Babuska和Osborn建立了(λh,uh)的误差估计.本文导出了σh的抽象误差估计式.并把该估计式应用于二阶椭圆特征值问题Raviart-Thomas混合有限元格式和重调和算子特征值问题Ciarlet-Raviart混合有限元格式,得到了一些新的误差估计. 相似文献
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在流线迎风Petrov-Galerkin(SUPG)稳定化有限元数值格式的基础上,结合时间方向的变分离散,构造对流反应扩散方程的稳定化时间间断时空有限元格式.该类格式在工程上有一些数值模拟应用,但相关文献没有看到类似数值格式的理论证明.本文以Radau点为节点,构造时间方向的Lagrange插值多项式,证明了稳定化有限元解的稳定性,时间最大模、空间L2(Ω)-模误差估计.文中利用插值多项式和有限元方法相结合的技巧,解耦时空变量,去掉了时空网格的限制条件,提供了时间间断稳定化时空有限元方法的理论证明思路,克服了因时空变量统一导致的实际计算时的复杂性. 相似文献
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In this paper, we consider the pressure projection stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the Stokes operator. The H1 and L2 error estimates for the velocity and the L2 error estimate for the pressure are obtained. Finally, the numerical results are displayed to verify the theoretical analysis. 相似文献
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The estimation of covariance matrices is central in array signal processing systems. This note addresses complex covariance estimation for the situation, where the complex data are available only as independent pairwise sets (observations) corresponding to individual elements of the matrix. The formulation for the empirical estimate and the normal maximum likelihood estimate is developed for the general case of different sample sizes for each observation. The approach allows, for example, the estimate of the p by p covariance matrix of a p-port sensor array from a two-port measurement instrument. 相似文献
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非定常Navier-Stokes方程的稳定化特征有限元法 总被引:1,自引:0,他引:1
1引言特征线有限元法是求解对流扩散问题的有效方法。在处理对流占优问题时,表现出了很好的稳定性[8]。对于求解Navier-Stokes方程,文[9]建立了特征有限元格式,并进行了详细分析,但得到的收敛阶O(h~m △t (h~(m 1)/△t))只是拟丰满的。文[10]对此作了非线性稳定性的进一步分析,给出了关于速度和压力的最优误差估计。但目前所有的特征有限元法都要求有限元空间满足inf-sup条件,这就排除了工程实际应用计算方便的低阶有 相似文献
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Mikko Lyly 《Numerische Mathematik》2000,85(1):77-107
Summary. We consider three triangular plate bending elements for the Reissner-Mindlin model. The elements are the MIN3 element of
Tessler and Hughes [19], the stabilized MITC3 element of Brezzi, Fortin and Stenberg [5] and the T3BL element of Xu, Auricchio
and Taylor [2, 17, 20]. We show that the bilinear forms of the stabilized MITC3 and MIN3 elements are equivalent and that
their implementation may be simplified by using numerical integration of reduced order. The T3BL element is shown to be essentially
the same as the MIN3 and stabilized MITC3 elements with reduced integration. We finally introduce a general stabilized finite
element formulation which covers all three methods. For this class of methods we prove the stability and optimal convergence
properties.
Received November 4, 1996 / Revised version received May 29, 1997 / Published online January 27, 2000 相似文献
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Silvia Bertoluzza 《Numerische Mathematik》2000,86(1):1-28
Summary. We propose here a stabilization strategy for the Lagrange multiplier formulation of Dirichlet problems. The stabilization
is based on the use of equivalent scalar products for the spaces and , which are realized by means of wavelet functions. The resulting stabilized bilinear form is coercive with respect to the
natural norm associated to the problem. A uniformly coercive approximation of the stabilized bilinear form is constructed
for a wide class of approximation spaces, for which an optimal error estimate is provided. Finally, a formulation is presented
which is obtained by eliminating the multiplier by static condensation. This formulation is closely related to the Nitsche's method for solving Dirichlet boundary value problems.
Received December 4, 1998 / Revised version received May 7, 1999 / Published online April 20, 2000 –? Springer-Verlag 2000 相似文献