共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper,a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established.Abstract lemmas for the error of the eigenvalue approximations are obtained.Based on the asymptotic error expansion formulas,the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from θ(h2) to θ(h4) when applying the lowest order Nédé1ec mixed finite element and a nonconforming mixed finite element.To our best knowledge,this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation.Numerical experiments are provided to demonstrate the theoretical results. 相似文献
2.
We propose and analyze the Ciarlet–Raviart mixed scheme for solving the biharmonic eigenvalue problem with bilinear finite
elements. We derive a higher order convergence rate for eigenvalue and eigenfunction approximations. Furthermore, we give
an asymptotic expansion of the eigenvalue error, from which an efficient extrapolation and an a posteriori error estimate
for the eigenvalue are given. Finally, numerical experiments illustrating the theoretical results are reported.
This author was supported by China Postdoctoral Sciences Foundation. 相似文献
3.
Wei Chen 《Numerical Methods for Partial Differential Equations》2005,21(3):512-520
Using the technique of eigenvalue error expansion and the technique of integral identities, we derive higher order convergence rate of the eigenvalue approximation for the biharmonic eigenvalue problem based on the Ciarlet‐Raviart discretization. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
4.
We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error analysis involved is shown to be affected by the nonlocal condition, which requires a suitable modification of the vector Lagrange interpolant on the overall finite element mesh. Nevertheless, we arrive at optimal error estimates. In the last section, an illustrative numerical example is given, which confirms the theoretical results. 相似文献
5.
In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain
full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions
for two nonconforming finite elements, Q
1rot and EQ
1rot. Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we
can improve the accuracy of the eigenvalue approximations.
This project is supported in part by the National Natural Science Foundation of China (10471103) and is subsidized by the
National Basic Research Program of China under the grant 2005CB321701. 相似文献
6.
考虑利用Q1元来求解Stokes特征值问题的误差渐进展开式,并以此为基础进行外推获得高精度. 相似文献
7.
In this paper we prove the existence of a deformation transforming an arbitrary open set into the ball, which has the following properties: it keeps constant the measure, the kth eigenvalue of Laplace–Dirichlet operator is continuous from the left and the first eigenvalue is decreasing. The deformation is given by a sequence of continuous Steiner symmetrizations, and the behavior of the eigenvalues is related to the stability of the Dirichlet problem. 相似文献
8.
Shanghui Jia Hehu Xie Xiaobo Yin Shaoqin Gao 《Numerical Methods for Partial Differential Equations》2008,24(2):435-448
In this paper, we analyze the biharmonic eigenvalue problem by two nonconforming finite elements, Q and E Q. We obtain full order convergence rate of the eigenvalue approximations for the biharmonic eigenvalue problem based on asymptotic error expansions for these two nonconforming finite elements. Using the technique of eigenvalue error expansion, the technique of integral identities, and the extrapolation method, we can improve the accuracy of the eigenvalue approximations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
9.
In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii~erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly. 相似文献
10.
《Mathematical Methods in the Applied Sciences》2018,41(10):3764-3778
In this paper, we present spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in a circular domain. First of all, we use the polar coordinate transformation and technique of separation of variables to reduce the problem to a sequence of equivalent 1‐dimensional eigenvalue problems that can be solved individually in parallel. Then, we derive the pole conditions and introduce weighted Sobolev space according to pole conditions. Together with the approximate properties of orthogonal polynomials, we prove the error estimates of approximate eigenvalues for each 1‐dimensional eigenvalue problem. Finally, we provide some numerical experiments to validate the theoretical results and algorithms. 相似文献
11.
在文献[1]中,作者M E Hochstenbach和B Plestenjak认为精化的方法不适合两参数特征值问题,原因是求解两参数特征值问题的精化方法存在着三个问题:即精化Ritz向量收敛性差,运算量大,不能计算多个特征值.本文指出,事实并非如此.针对右定两参数特征值问题,本文提出了一种有效的精化数值方法.并通过理论证明和数值实验说明了Ritz值的收敛性,以及精化Ritz向量具有比通常的Ritz向量更好的收敛性. 相似文献
12.
We study a model boundary-value problem for the Laplacian in the unit disk with closely-spaced and periodic alternation of the type of boundary condition for the case in which the Dirichlet problem is the limit one. We study and justify the two-parameter asymptotics of an eigenvalue of the perturbed problem converging to a simple eigenvalue of the limit problem. 相似文献
13.
本文讨论一类具有特殊结构的Jacobi矩阵的特征值反问题,该问题由描述变截面杆的微分方程离散化得到.我们得到了这个问题有解的一些必要条件,并且通过一些数值例子,说明了L.Lu和K.Michael给出的充分条件和算法在矩阵的阶数高于3的时候是错误的。 相似文献
14.
Yoshinori Miyazaki Yasushi Kikuchi DongSheng Cai Yasuhiko Ikebe. 《Mathematics of Computation》2001,70(235):1195-1204
In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their derivatives may be reformulated as the eigenvalue problem for infinite matrices. Approximation by truncation is justified but no error estimates are given there.
The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown.
In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.
15.
讨论了关于斜对称双对角矩阵的特征值反问题.即:已知一个n阶斜对称双对角矩阵的特征值和两个n-1阶子矩阵的部分特征值,则可求得该矩阵.最后给出了数值例子. 相似文献
16.
Vadim Kaushansky Alexander Lipton Christoph Reisinger 《Applied Mathematical Finance》2013,20(5-6):434-465
ABSTRACTWe derive a semi-analytical formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the boundary condition. We discuss and test several computational methods to solve a finite-dimensional approximation to this nonlinear eigenvalue problem. Finally, we apply our results to the computation of default probabilities and credit valuation adjustments in a structural credit model with mutual liabilities. 相似文献
17.
Minimization of the ground state of the mixture of two conducting materials in a small contrast regime 下载免费PDF全文
Carlos Conca Marc Dambrine Rajesh Mahadevan Duver Quintero 《Mathematical Methods in the Applied Sciences》2016,39(13):3549-3564
We consider the problem of distributing two conducting materials with a prescribed volume ratio in a given domain so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions. The gap between the two conductivities is assumed to be small (low contrast regime). For any geometrical configuration of the mixture, we provide a complete asymptotic expansion of the first eigenvalue. We then consider a relaxation approach to minimize the second‐order approximation with respect to the mixture. We present numerical simulations in dimensions two and three to illustrate optimal distributions and the advantage of using a second‐order method. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
19.
非局部边界条件的特征问题及发展问题 总被引:2,自引:0,他引:2
考虑在有界区域中非局部边界条件的椭圆特征值问题 ,边界条件与特征值的关系 ,以及在合理假设条件下相应的发展问题的上下解的收敛问题 相似文献
20.
A kind of generalized inverse eigenvalue problem is proposed which includes the additive, multiplicative and classical inverse eigenvalue problems as special cases. Newton's method is applied, and a local convergence analysis is given for both the distinct and the multiple eigenvalue cases. When the multiple eigenvalues are present we show how to state the problem so that it is not over-determined, and discuss a Newton-method for the modified problem. We also prove that the modified method retains quadratic convergence, and present some numerical experiments to illustrate our results. © 1997 by John Wiley & Sons, Ltd. 相似文献