对流扩散特征值问题的自适应间断有限元方法  

THE ADAPTIVE DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EIGENVALUE PROBLEMS

作　　者：段丽梅 陈兴龙 韩家宇 DUAN Li-mei;CHEN Xing-long;HAN Jia-yu(School of Mathematics Science,Guizhou Normal University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《数学杂志》2023年第6期515-528,共14页Journal of Mathematics

基　　金：国家自然科学基金青年项目(12001130);贵州省科技计划项目(黔科合-ZK[2021]012)。

摘　　要：本文研究了对流扩散特征值问题的间断有限元方法.对流扩散方程作为偏微分方程一个重要的分支,源于环境科学、流体力学、空气动力学等诸多实际物理背景中,由于对流扩散方程的解很难通过解析的方法得到,所以探索对流扩散方程的数值方法具有重要的价值.对流扩散特征值问题的数值方法是当前计算数学界的热点.该研究的困难之处在于该问题的非对称性和对流项导致的边界层效应.本文利用间断有限元法方法研究对流扩散特征值问题,获得了该方法的完整的后验误差估计结果,并进行了自适应有限元计算.数值实验结合理论分析表明我们的方法达到了最优收敛阶.The discontinuous finite element method for convection-diffusion eigenvalue problems is studied in this paper.As an important branch of partial differential equation,the convection-diffusion equation originates from many practical physical backgrounds,such as envi-ronmental science,fluid mechanics,aerodynamics,etc.Since the solution of convection-diffusion equation is difficult to be obtained by the analytical method,it is of great value to explore the numerical method of convection-diffusion equation.The numerical method of convection-diffusion eigenvalue problem is a hot topic in computational mathematics.The difficulty of this study lies in the asymmetry of the problem and the boundary layer effect caused by the convective term.In this paper,the discontinuous finite element method is used to study the convection-diffusion eigenvalue problem.The complete posterior error estimation results of this method are obtained and the adaptive finite element calculation is performed.Numerical experiments and theoretical analysis show that our method reaches the optimal convergence order.

关 键 词：对流扩散特征值 间断有限元方法 后验误差 自适应计算 

分 类 号：O241.82[理学—计算数学]