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

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.

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

“…On the basis of the homogenization method, He and Cui et al established an SSOTS analysis method to predict the physical and mechanical performance of the composite structure through introducing a random sample model. [17][18][19][20][21] However, the theoretical verification is not enough for the random composites. [20] Meanwhile, Jikov et al [16] proved the existences of the homogenized coefficients and the homogenized solution for the randomly distributed composite.…”