摘要:对流扩散方程是偏微分方程一个很重要的分支并且在许多领域都有广泛的应用，对流扩散方程特征值问题的数值方法的研究有重要的实际应用，所以这也是前计算数学界的热点，本文研究了对流扩散特征值问题的hp- 局部不连续断伽辽金方法(LDG)，通过分析得到了先验误差估计，即关于网格尺寸h 是最优以及关于p 是次优的hp- 误差估计，并且进行了相应的数值实验。

Abstract:Convection-diffusion equation is a very important branch of partial differential equation and is widely used in many fields, The study of numerical methods for eigenvalue problems of convection-diffusion equation has important practical applications, so it is also a hot spot in pre-computational mathematics, In this paper, the hp-local discontinuous discontinuity Galerkin method (DG) for convection-difusion eigenvalue problems is studied, and the prior error estimates, that is, the hp-error estimates about the mesh size h is optimal and p is suboptimal, are obtained through analysis, and the corresponding numerical experiments are carried out.