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41.
M. A. Efendiev J. Fuhrmann S. V. Zelik 《Mathematical Methods in the Applied Sciences》2004,27(8):907-930
For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
42.
In this paper, a unified approach for analysing finite dimensional approximations to a class of partial differential equations boundary value problems (second‐kind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
43.
美式期权定价中非局部问题的有限元方法 总被引:2,自引:1,他引:1
在本文中 ,我们关心的是美式期权的有限元方法 .首先 ,根据 [4 ]我们对所讨论的问题引进一个新奇的实用的方法 ,它涉及到对原问题重新形成准确的数学公式 ,使得数值解的计算可以在非常小的区域上进行 ,从而该算法计算速度快精度高 .进而 ,我们利用超逼近分析技术得到了有限元解关于 L2 -模的最优估计 . 相似文献
44.
45.
46.
A. Debussche 《Journal de Mathématiques Pures et Appliquées》1998,77(10):967-988
The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension. 相似文献
47.
G.N. Gatica 《Applied Mathematics Letters》1997,10(6):29-35
We study the solvability and Galerkin approximation of an exterior hyperelastic interface problem arising in plane elasticity. The weak formulation is obtained from an appropriate combination of a mixed finite element approach with a Dirichlet-to-Neumann method. The derivation of our results is based on some tools from nonlinear functional analysis and the Babuska-Brezzi theory for variational problems with constraints. 相似文献
48.
Gr-凝聚环的分次FP-内射维数 总被引:4,自引:0,他引:4
引进了分次FP-内射维数,对Gr-凝聚环的分次FP-内射维数作了刻划,将Stentrom等人的若干工作推广到分次环上. 相似文献
49.
Houman Borouchaki Abdelhakim Cherouat Patrick Laug Khemais Saanouni 《Comptes Rendus Mecanique》2002,330(10):709-716
The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716. 相似文献
50.
Understanding of the basic nature of arc root fluctuation is still one of the unsolved problems in thermal arc plasma physics.
It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc
root behavior has been reported through the analysis of voltages, acoustic and optical signals which are generated from a
hollow copper electrode arc plasma torch. In this paper we present details of computations involved in the estimation process
of various dynamic properties and show how they reflect chaotic behavior of arc root in the system. 相似文献