Convergence rates in homogenization of parabolic systems with locally periodic coefficients

2020/07/08 by Yao Xu, Xu, Yao
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2007.03853

Abstract

In this paper we study the quantitative homogenization of second-order parabolic systems with locally periodic (in both space and time) coefficients. The O(ε) scale-invariant error estimate in L²(0, T; L^(2d)/(d-1)(Ω)) is established in C^{1, 1} cylinders under minimum smoothness conditions on the coefficients. This process relies on critical estimates of smoothing operators. We also develop a new construction of flux correctors in the parabolic manner and a sharp estimate for temporal boundary layers.

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