ANALYSIS OF THE MULTISCALE FINITE ELEMENT METHOD FOR NONLINEAR AND RANDOM HOMOGENIZATION PROBLEMS

ZHANGXIN CHEN; TATYANA Y. SAVCHUK

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ANALYSIS OF THE MULTISCALE FINITE ELEMENT METHOD FOR NONLINEAR AND RANDOM HOMOGENIZATION PROBLEMS

机译：非线性与随机均质化问题的多尺度有限元分析

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In this paper we study the convergence of the multiscale finite element method for nonlinear and random homogenization problems. Error estimates similar to those for linear homogenization problems are obtained here.

机译：在本文中，我们研究了非线性和随机均质化问题的多尺度有限元方法的收敛性。在这里获得了与线性均质化问题相似的误差估计。

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《SIAM Journal on Numerical Analysis》 |2009年第1期|共20页
作者
ZHANGXIN CHEN; TATYANA Y. SAVCHUK;
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正文语种 eng
中图分类数值分析;
关键词
multiscale problem; multiscale finite element method; finite element; nonlinear problems; random problems; oversampling technique; convergence; stability; error estimate;

机译：多尺度问题;多尺度有限元方法;有限元;非线性问题;随机问题;过采样技术;收敛性;稳定性;误差估计;

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专利

1. ANALYSIS OF THE MULTISCALE FINITE ELEMENT METHOD FOR NONLINEAR AND RANDOM HOMOGENIZATION PROBLEMS [J] . ZHANGXIN CHEN, TATYANA Y. SAVCHUK SIAM Journal on Numerical Analysis . 2009,第1期

机译：非线性与随机均质化问题的多尺度有限元分析
2. FINITE ELEMENT HETEROGENEOUS MULTISCALE METHOD FOR NONLINEAR MONOTONE PARABOLIC HOMOGENIZATION PROBLEMS [J] . Abdulle Assyr, Huber Martin E. ESAIM. Mathematical modelling and numerical analysis . 2016,第6期

机译：非线性单调抛物线均质化问题的有限元异质多尺度方法
3. Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-carlo method [J] . Juan Ma, Jie Zhang, Liangjie Li, Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods . 2014,第6期

机译：基于有限元法和蒙特卡洛法的微观结构中具有完全随机性和相关性的异质材料的随机均质分析
4. Finite Element Computational Homogenization of Nonlinear Multiscale Materials in Magnetostatics [C] . I. Niyonzima, R. V. Sabariego, P. Dular, International Conference on the Computation of Electromagnetic Fields . 2011

机译：磁静磁带中非线性多尺度材料的有限元计算均匀化
5. Numerical analysis of homogenization using random finite element method. [D] . Paiboon, Jumpol. 2013

机译：使用随机有限元方法对均质化的数值分析。
6. Full Discretisations for Nonlinear Evolutionary Inequalities Based on Stiffly Accurate Runge–Kutta and hp-Finite Element Methods [O] . J. Gwinner, M. Thalhammer -1

机译：基于严格精确的Runge-Kutta和hp-有限元方法的非线性演化不等式的完全离散化
7. Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems [O] . Assyr Abdulle, Martin E. Huber 2016

机译：非线性单调抛物型均质化问题的有限元异质多尺度方法

ANALYSIS OF THE MULTISCALE FINITE ELEMENT METHOD FOR NONLINEAR AND RANDOM HOMOGENIZATION PROBLEMS

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