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| Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations | |
| 作者姓名： | 罗振东 周艳杰 朱江 |
| 作者单位： | School of Science Beijing Jiaotong University，Beijing Technology and Business University，Institute of Atmospheric Physics，Chinese Academy of Sciences，Beijing 100044，P. R. China Institute of Atmospheric Physics，Chinese Academy of Sciences，Beijing 100029，P. R. China，Beijing 100037，P. R. China，Beijing 100029，P. R. China |
| 基金项目： | 国家自然科学基金;北京交通大学校科研和教改项目 |
| 摘 要： | 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. |
| 关 键 词： | 汽相沉积 化学反应方程 离散表述 混合有限元法 |
| 收稿时间： | 2006-03-28 |
| 修稿时间： | 2006-11-29 |
Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations |
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| Luo?Zhen-dong,Zhou?Yan-jie,Zhu?Jiang.Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations[J].Applied Mathematics and Mechanics(English Edition),2007,28(5):665-675. | |
| Authors: | Luo?Zhen-dong Zhou?Yan-jie Zhu?Jiang |
| Institution: | 1. School of Science,Beijing Jiaotong University,Beijing 100044,P.R.China;Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,P.R.China 2. Beijing Technology and Business University,Beijing 100037,P.R.Chma 3. Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,P.R.China |
| 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. |
| Keywords: | vapor deposition chemical reaction equation the mixed finite element method semidiscrete formulation fully discrete formulation |
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