LUO Zhen-dong, ZHOU Yan-jie, ZHU Jiang. Research of Discrete Formulation of Mixed Finite Element Methods for the Vapor Deposition Chemical Reaction Equations[J]. Applied Mathematics and Mechanics, 2007, 28(5): 592-602.
 Citation: LUO Zhen-dong, ZHOU Yan-jie, ZHU Jiang. Research of Discrete Formulation of Mixed Finite Element Methods for the Vapor Deposition Chemical Reaction Equations[J]. Applied Mathematics and Mechanics, 2007, 28(5): 592-602.

# Research of Discrete Formulation of Mixed Finite Element Methods for the Vapor Deposition Chemical Reaction Equations

• Rev Recd Date: 2007-01-16
• Publish Date: 2007-05-15
• 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 meaning,but also of extremely extensive applied vistas.
•  [1] 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. [2] 罗振东.非线性发展方程和热传导-对流扩散方程混合有元方法的分析与应用研究[D].博士学位论文.合肥:中国科学技术大学,1996. [3] Ciarlet P G.The Finite Element Method for Elliptic Problems[M].Amsterdam: North-Holland, 1978. [4] TANG Xian-jiang.On the existence and uniqueness of the solution to the Navier-Stokes equations[J].Acta Matematica Scientia,1995,15(3)：342-351. [5] Teman R.Navier-Stokes Equation(3rd)[M].Amsterdam,New york: North-Holland, 1984. [6] 罗振东. 混合有限元法基础及其应用[M]. 北京：科学出版社，2006. [7] 李开泰,黄艾香. 有限元方法及其应用[M]. 北京：科学出版社,2006.

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