Li R H, Chen Z Y, Wu W. Generalized Difference Methods for Differential Equations-Numerical Analysis of Finite Volume Methods[M]. New York: Marcel Dekker Inc, 2000.
[4]
Holmes P, Lumley J L, Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry[M]. Cambridge: Cambridge University Press, 1996.
[5]
Fukunaga K. Introduction to Statistical Recognition[M]. New York: Academic Press, 1990.
[6]
Jolliffe I T. Principal Component Analysis[M]. Berlin: Springer-Verlag, 2002.
[7]
Selten F. Baroclinic empirical orthogonal functions as basis functions in an atmospheric model[J]. J. Atmosph. Sci., 1997, 54: 2099-2114. 2.0.CO;2 target="_blank">
[8]
Sirovich L. Turbulence and the dynamics of coherent structures: Part I-III[J]. Quart. Appl. Math., 1987, 45: 561-590.
[9]
Luo Z D, Xie Z H, Shang Y Q, Chen J. A reduced finite volume element formulation and numerical simulations based on POD for parabolic equations[J]. J. Comput. Appl. Math., 2011, 235(8): 2098-2111.
[10]
Adams R A. Sobolev Spaces[M]. New York: Academic Press, 1975.
[11]
罗振东. 混合有限元法基础及其应用[M]. 北京: 科学出版社, 2006.
[12]
Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Philadelphia: Society for Industrial and Applied Mathematic, 2002.
[13]
Rudin W. Functional and Analysis (2nd Ed.)[M]. New York: McGraw-Hill Companies, Inc. 1973.
[14]
Luo Z D, Li H, Zhou Y J, Huang X M. A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem[J]. J. Math. Anal. Appl., 2012, 385: 310-321.
[15]
Luo Z D, Li H, Sun P. A reduced Crank-Nicolson finite volume element formulation based on POD for parabolic problems[J]. Appl. Math. Comput., 2013, 219(11): 5887-5900.
[16]
Luo Z D, Li H, Sun P, An J, Navon I M. A reduced finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems[J]. Math. Comput. Simul., 2013, 89: 50-68.
