Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients
作者： Hao Dong , Yu-Feng Nie , Jun-Zhi Cui , Ya-Tao Wu
DOI: 10.1088/1674-1056/24/9/090204
关键词:
摘要: We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by multiscale analysis. In addition, we theoretically explain importance of solution error analysis in pointwise sense. associated explicit convergence rates also obtained. Then a numerical method based on Newmark scheme is presented to solve equations. Finally, some examples used verify effectiveness and efficiency algorithm proposed.
harvard.edu
sci-hub.se 参考文章(20)
Zi-Hao Yang, Yun Chen, Zhi-Qiang Yang, Qiang Ma, Dynamic thermo-mechanical coupled response of random particulate composites: A statistical two-scale method Chinese Physics B. ,vol. 23, pp. 076501- ,(2014) , 10.1088/1674-1056/23/7/076501
YT Wu, YF Nie, ZH Yang, None, Comparison of Four Multiscale Methods for EllipticProblems Cmes-computer Modeling in Engineering & Sciences. ,vol. 99, pp. 297- 325 ,(2014) , 10.3970/CMES.2014.099.297
Alois Kutner, Anna-Margarete Sändig, Nonlinear Differential Equations ,(1980)
Dietrich Braess, Finite Elements Cambridge University Press. ,(2007) , 10.1017/CBO9780511618635
Zhen Wang, Jingqing Zhou, Hugo Loaiciga, Huaicheng Guo, Song Hong, A DPSIR model for ecological security assessment through indicator screening: a case study at Dianchi Lake in China. PLOS ONE. ,vol. 10, ,(2015) , 10.1371/JOURNAL.PONE.0131732
Liqing Lu, Shengjia Li, Higher order energy decay for damped wave equations with variable coefficients Journal of Mathematical Analysis and Applications. ,vol. 418, pp. 64- 78 ,(2014) , 10.1016/J.JMAA.2014.03.081
C. Timofte, Michail D. Todorov, Christo I. Christov, On the Homogenization of a Damped Wave Equation APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: Proceedings of the 2nd International Conference. ,vol. 1301, pp. 543- 550 ,(2010) , 10.1063/1.3526656
Gabriel Nguetseng, Hubert Nnang, Nils Svanstedt, Asymptotic Analysis for a Weakly Damped Wave Equation with Application to a Problem Arising in Elasticity Journal of Function Spaces and Applications. ,vol. 8, pp. 17- 52 ,(2010) , 10.1155/2010/291670
Qiao-Li Dong, Li-Qun Cao, Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients Applied Numerical Mathematics. ,vol. 59, pp. 3008- 3032 ,(2009) , 10.1016/J.APNUM.2009.07.008
Jun-Zhi Cui, Li-Qun Cao, Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains Numerische Mathematik. ,vol. 96, pp. 525- 581 ,(2004) , 10.1007/S00211-003-0468-7