Research of Discrete Formulation of Mixed Finite Element Methods for the Vapor Deposition Chemical Reaction Equations
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摘要: 蒸汽沉淀化学反应过程有着极其广泛的应用，其数学模型归结为一个包含流速场，温度场,压力场和气体溶质场的非线性偏微分方程组．用混合有限元方法研究蒸汽沉淀化学反应方程组,导出其半离散化和全离散化的混合元格式，并证明这些格式的解的存在性和收敛性(误差估计)．用混合元法处理究蒸汽沉淀化学反应方程组,可以同时求出流速场，温度场，压力场和气体溶质场的数值解. 因此该研究既具有重要的理论意义，又具有广泛的应用前景．
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关键词:
- 化学蒸汽沉淀反应方程 /
- 混合元方法 /
- 半离散化格式 /
- 全离散化格式
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 meaning,but also of extremely extensive applied vistas. -
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