Communications in Mathematical Sciences

Volume 10 (2012)

Number 3

Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients

Pages: 945 – 976

DOI: https://dx.doi.org/10.4310/CMS.2012.v10.n3.a11

Authors

Houde Han (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Zhiwen Zhang (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Abstract

We develop a multiscale tailored finite point method (MsTFPM) for second order elliptic equations with rough or highly oscillatory coefficients. The finite point method has been tailored to some particular properties of the problem, so that it can capture the multiscale solutions using coarse meshes without resolving the fine scale structure of the solution. Several numerical examples in one- and two-dimensions are provided to show the accuracy and convergence of the proposed method. In addition, some analysis results based on the maximum principle for the one- dimensional problem are proved.

Keywords

tailored finite point method (TFPM), multiple scales, maximum principle, rough coefficients, elliptic. equations

2010 Mathematics Subject Classification

35J25, 35Nxx, 65Yxx

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Published 9 April 2012