Abstract
The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element (MFE) method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence (error estimate) of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.
Similar content being viewed by others
References
Ly H V, Tram H T. Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor[J]. Quarterly of Applied Mathematics, 2002, 60(3):631–656.
Luo Zhendong. Analysis and applied study mixed finite element methods for nonlinear evolution equation and conduction-convection diffuse equations[D]. Ph D Dissertation, University of Science and Technology of China, Hefei, 1996 (in Chinese).
Ciarlet P G. The finite element method for elliptic problems[M]. Amsterdam: North-Holland, 1978.
Tang Xianjiang. On the existence and uniqueness of the solution to the Navier-Stokes equations[J]. Acta Matematica Scientia, 1995, 15(3):342–351.
Teman R. Navier-Stokes equation[M]. 3rd Edition. Amsterdam, New York: North-Holland, 1984.
Luo Zhendong. Mixed finite element methods and applications[M]. Beijing: Chinese Science Press, 2006 (in Chinese).
Li Kaitai Huang Aixiang. Finite element methods and applications[M]. Beijing: Chinese Science Press, 2006 (in Chinese).
Author information
Authors and Affiliations
Corresponding author
Additional information
(Communicated by LIN Jian-zhong)
Project supported by the National Natural Science Foundation of China (Nos.10471100 and 40437017) and the Science and Technology Foundation of Beijing Jiaotong University
Rights and permissions
About this article
Cite this article
Luo, Zd., Zhou, Yj. & Zhu, J. Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations. Appl Math Mech 28, 665–675 (2007). https://doi.org/10.1007/s10483-007-0511-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-007-0511-z
Key words
- vapor deposition chemical reaction equation
- the mixed finite element method
- semidiscrete formulation
- fully discrete formulation