LINEARIZED NUMERICAL HOMOGENIZATION METHOD FOR NONLINEAR MONOTONE PARABOLIC MULTISCALE PROBLEMS

被引：9
作者：
Abdulle, A. [1 ]
Huber, M. E. [1 ]
Vilmart, G. [2 ]
机构：
[1] Ecole Polytech Fed Lausanne, Math Sect, ANMC, CH-1015 Lausanne, Switzerland
[2] Univ Geneva, Sect Math, CH-1211 Geneva 4, Switzerland
来源：
MULTISCALE MODELING & SIMULATION | 2015年 / 13卷 / 03期
基金：
瑞士国家科学基金会;
关键词：
monotone parabolic multiscale problem; linearized scheme; numerical homogenization method; fully discrete a priori error estimates; FINITE-ELEMENT APPROXIMATION; BOUNDARY-VALUE-PROBLEMS; COMPUTATIONAL HOMOGENIZATION; TIME DISCRETIZATION; ELLIPTIC PROBLEMS; CONVERGENCE; EQUATIONS; OPERATORS; SYSTEMS;
D O I：
10.1137/140975504
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the microscopic scales. It can be interpreted as a linearized version of a standard nonlinear homogenization method. We prove the stability of the method and derive optimal a priori error estimates which are fully discrete in time and space. Numerical experiments confirm the error bounds and illustrate the efficiency of the method for various nonlinear problems.
引用
收藏
页码：916 / 952
页数：37
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