Abstract: A Local Discontinuous Galerkin finite element method（LDG method） is presented for one-dimensional convection diffusion equations with first boundary conditions with constant coefficients. It is proved that the LDG method is stable for convection diffusion equations with first boundary conditions with constant coefficients. Numerical examples verify the correctness of the theoretical analysis.

Key words: Local Discontinuous Galerkin finite element（LDG） method;first boundary conditions, stability, convection diffusion equations

摘要： 针对一维常系数对流扩散模型方程，讨论了当含有第一类边界条件时，局部间断有限元方法（LDG方法）的稳定性。利用有限元理论基本分析技巧，证明了当边界条件为第一类的边界条件时，LDG方法为稳定的，并利用数值算例证明理论分析的正确性。

关键词: 局部间断Galerkin有限元（LDG）方法, 第一类边界条件, 稳定性, 对流扩散方程