二维区域上椭圆均匀化问题的收敛率

doi:10.13371/j.cnki.chin.q.j.m.2017.03.007

数学季刊 ›› 2017, Vol. 32 ›› Issue (3): 277-293.doi: 10.13371/j.cnki.chin.q.j.m.2017.03.007

二维区域上椭圆均匀化问题的收敛率

College of Science, Zhongyuan University of Technology

收稿日期:2016-07-13 出版日期:2017-09-30 发布日期:2020-10-22
作者简介:ZHAO Jie(1983-), male, native of Kaifeng, Henan, a lecturer of Zhongyuan University of Technology, Ph.D., engages in partial of di®erential equations; WANG Juan(1984-), female, native of Shangqiu, Henan, a lecturer of Zhongyuan University of Technology, Ph.D., engages in image processing.
基金资助:
Supported by the NNSF of Chian(11626239,11626238)； Supported by the Natural Science Foundation of Henan

Province(152300410227)；

Convergence Rates for Elliptic Homogenization Problems in Two-dimensional Domain

College of Science, Zhongyuan University of Technology

Received:2016-07-13 Online:2017-09-30 Published:2020-10-22
About author:ZHAO Jie(1983-), male, native of Kaifeng, Henan, a lecturer of Zhongyuan University of Technology, Ph.D., engages in partial of di®erential equations; WANG Juan(1984-), female, native of Shangqiu, Henan, a lecturer of Zhongyuan University of Technology, Ph.D., engages in image processing.
Supported by:
Supported by the NNSF of Chian(11626239,11626238)； Supported by the Natural Science Foundation of Henan Province(152300410227)；

摘要/Abstract

摘要： In this paper, we study the convergence rates of solutions for second order elliptic equations with rapidly oscillating periodic coefficients in two-dimensional domain. We use an extension of the "mixed formulation" approach to obtain the representation formula satisfied by the oscillatory solution and homogenized solution by means of the particularity of solutions for equations in two-dimensional case. Then we utilize this formula in combination with the asymptotic estimates of Green or Neumann functions for operators and uniform regularity estimates of solutions to obtain convergence rates in Lp for solutions as well as gradient error estimates for Dirichlet or Neumann problems respectively.

关键词: Homogenization, Convergence rates, Green functions, Neumann functions

Abstract: In this paper, we study the convergence rates of solutions for second order elliptic equations with rapidly oscillating periodic coefficients in two-dimensional domain. We use an extension of the "mixed formulation" approach to obtain the representation formula satisfied by the oscillatory solution and homogenized solution by means of the particularity of solutions for equations in two-dimensional case. Then we utilize this formula in combination with the asymptotic estimates of Green or Neumann functions for operators and uniform regularity estimates of solutions to obtain convergence rates in Lp for solutions as well as gradient error estimates for Dirichlet or Neumann problems respectively.

Key words: Homogenization, Convergence rates, Green functions, Neumann functions

中图分类号:

O175.25

赵杰, 李红, 王娟. 二维区域上椭圆均匀化问题的收敛率[J]. 数学季刊, 2017, 32(3): 277-293.

ZHAO Jie, LI Hong, WANG Juan. Convergence Rates for Elliptic Homogenization Problems in Two-dimensional Domain[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(3): 277-293.

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二维区域上椭圆均匀化问题的收敛率

Convergence Rates for Elliptic Homogenization Problems in Two-dimensional Domain

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