Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

doi:10.1088/1674-1056/24/9/090204

Abstract We study the hyperbolic-parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.

Keywords: hyperbolic-parabolic equations rapidly oscillating coefficients second-order two-scale numerical method Newmark scheme

Received: 15 March 2015
Revised: 22 April 2015
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.60.Cb	(Numerical simulation; solution of equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11471262), the National Basic Research Program of China (Grant No. 2012CB025904), and the State Key Laboratory of Science and Engineering Computing and the Center for High Performance Computing of Northwestern Polytechnical University, China.

Corresponding Authors: Nie Yu-Feng
E-mail: yfnie@nwpu.edu.cn

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Dong Hao (董灏), Nie Yu-Feng (聂玉峰), Cui Jun-Zhi (崔俊芝), Wu Ya-Tao (武亚涛) Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients 2015 Chin. Phys. B 24 090204

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Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

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