Quadratic finite volume element method for the air pollution model

References

• Adams, R. A. , 1975. Sobolev Spaces . New York: Academic Press; 1975.
   Google Scholar
• Blom, J. G. , and Verwer, J. G. , 2000. A Comparison of integration methods for atmospheric transport-chemistry problems , J. Comput. Appl. Math. 126 (2000), pp. 381–396.
   Web of Science ®Google Scholar
• Botchev, M. A. , and Verwer, J. G. , 2003. A new approximate matrix factorization for implicit time integration in air pollution modeling , J. Comput. Appl. Math. 157 (2003), pp. 309–327.
   Web of Science ®Google Scholar
• Cai, Z. Q. , 1991. On the finite Volume element methods , Numer. Math 58 (1991), pp. 713–735.
   Web of Science ®Google Scholar
• Chen, Z. Y. , 1990. The generalized difference method for the heat conductor equation , J. Zhongshan Univ.(Natural Sciences) 29 (1990), pp. 6–13, (in Chinese).
   Google Scholar
• Dimov, I. , Georgiev, K. , Ostromsky, T. Z. , and Zlatev, Z. , 2004. Computational challenges in the numerical treatment of large air pollution models , Ecol. Model. 179 (2004), pp. 187–203.
   Web of Science ®Google Scholar
• Guo, S. B. , and Zhang, Z. Y. , 2007. Numerical methods based on characteristic centered finite difference procedure for a class of nonlinear evolution equations , Chin. J. Comput. Phys. 24 (2007), pp. 637–646, (in Chinese).
   Google Scholar
• Hao, J. M. , and Ma, G. D. , 1989. The Project of Air Pollution Control . Beijing: Higher Education Press; 1989, (in Chinese).
   Google Scholar
• Huang, S. X. , and Wu, R. S. , 2001. Mathematical Physics Problems in the Atmospheric Science . Beijing: Meteorological Press; 2001, (in Chinese).
   Google Scholar
• Li, D. Y. , and Chen, G. N. , 1995. An Introduction of the Difference Method for the Parabolic Equation . Beijing: Science Press; 1995, (in Chinese).
   Google Scholar
• Li, R. H. , Chen, Z. Y. , and Wu, W. , 2000. Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods . NewYork: Marcel Dekker; 2000.
   Google Scholar
• Li, J. P. , and Chou, J. F. , 2003. The development of the nonlinear atmospheric dynamics , Chin. J. Atmos. Sci. 27 (2003), pp. 653–673, (in Chinese).
   Google Scholar
• Mu, M. , and Zhang, Z. Y. , 2006. Conditional nonlinear optimal perturbations of a two-dimensional quasigeostrophic model , J. Atmos. Sci. 63 (2006), pp. 1587–1604.
   Web of Science ®Google Scholar
• Tian, M. Z. , and Chen, Z. Y. , 1991. The generalized difference method for the elliptic equation(quadratic element) , Chin. J. Numer. Math. 13 (1991), pp. 99–113, (in Chinese).
   Google Scholar
• Wang, B. , and Ji, Z. Z. , 2006. The New Numerical Method and its Applications in the Atmospheric Science . Beijing: Science Press; 2006, (in Chinese).
   Google Scholar
• Wang, Z. F. , and Zhang, Z. Y. , 2007. The characteristic finite volume element methods for the two-dimensional generalized nerve conduction equation , Neural Parallel Sci.Comput. 15 (2007), pp. 27–43.
   Google Scholar
• Wu, W. , 1987. The error estimate of the generalized difference method for the nonlinear parabolic equation , Math. Numer. Sin. 2 (1987), pp. 119–132, (in Chinese).
   Google Scholar
• Yang, M. , 2004. Quadratic finite volume methods for nonlinear parabolic equations , Chin. J. Numer. Math. 26 (2004), pp. 257–266, (in Chinese).
   Google Scholar
• Yu, D. H. , and Tang, H. Z. , 2003. The Numerical Method of the Differential Equation . Beijing: Science Press; 2003, (in Chinese).
   Google Scholar
• Yuan, G. W. , 2000. Uniqueness and stability of difference solution with nonuniform meshes for nonlinear parabolic systems , Math. Numer. Sin 22 (2000), pp. 139–150, (in Chinese).
   Google Scholar
• Zhang, Z. , 2009. Error estimates of finite volume element method for the pollution in groundwater flow , Numer. Methods Partial Differential Equations 25 (2009), pp. 259–274.
   Web of Science ®Google Scholar
• Zhang, Z. Y. , and Lin, J. , 2007. Dynamics of Jovian atmospheres with applications of nonlinear singular vector method , Internet J. Numer. Methods in Fluids 55 (2007), pp. 713–721.
   Web of Science ®Google Scholar
• Zhou, Y. L. , Shen, L. J. , and Yuan, G. W. , 1997. Finite difference method of first boundary problem for quasi-linear parabolic system, IV: Iterative astringency , Sci. China Ser. A 27 (1997), pp. 322–327, (in Chinese).
   Google Scholar
• Zhou, Y. L. , and Yuan, G. W. , 1997. The general finite difference scheme has parallel property for quasi-linear parabolic system , Sci. China Ser.A 27 (1997), pp. 105–111, (in Chinese).
   Google Scholar
• Zlatev, Z. , 1995. Computer Treatment of Large Air Pollution Models . Dordrecht: Kluwer Academic Publishers; 1995.
   Google Scholar