Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations  

作　　者：罗振东 周艳杰 朱江 

机构地区：[1]School of Science,Beijing Jiaotong University [2]Beijing Technology and Business University [3]Institute of Atmospheric Physics,Chinese Academy of Sciences

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第5期665-675,共11页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos.10471100 and 40437017);the Science and Technology Foundation of Beijing Jiaotong University

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.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：vapor deposition chemical reaction equation the mixed finite element method semidiscrete formulation fully discrete formulation 

分 类 号：O241.82[理学—计算数学]