应用数学2020，Vol.33Issue(2)：275-294,20.
对流反应扩散方程的SUPG稳定化时空有限元解的误差估计
Error Estimations of SUPG Stabilized Space-Time Finite Element Approximations for Convection-Diffusion-Reaction Equations
摘要
Abstract
A kind of fully discrete version of stabilized space-time finite element approximate scheme for the convection-diffusion-reaction equations is established by combining the space-time finite element discretization with the streamline upwind Petrov-Galerkin method(SUPG).The formulations discussed in this paper is different from traditional SUPG method.The discrete variation forms were used in both time and space directions in order to derive high order accuracy schemes,especially high accuracy in time.The theoretical proofs of this kind of scheme were difficult to find in relative references,although there are some simulations in practical applications studied by engineers.We focus on presenting the proof of stability and error estimates of the approximate solutions.The techniques of combining the Gauss-Legendre and Gauss-Lobatto integration rules with the finite element method was used.The conditions on the space-time meshes are removed,the space and time variables are decoupled.This kind of decoupling can overcome the high dimensional difficulties and complexities in both theoretical analysis and practical computations caused by unifying the space and time variables when established the scheme.And the idea of the proof without introducing dual problem presented here will build up the theoretical foundations of the stabilized SUPG space-time finite element scheme.关键词
稳定化时空有限元方法/SUPG方法/对流扩散反应方程/高斯积分准则/误差估计Key words
Stabilized space-time finite element method/SUPG method/Convection diffusion reaction equation/Gauss integration rule/Error estimation分类
数理科学引用本文复制引用
林嘉斌,李宏,董自明,赵智慧..对流反应扩散方程的SUPG稳定化时空有限元解的误差估计[J].应用数学,2020,33(2):275-294,20.基金项目
Supported by the National Natural Science Foundation of China (11761053),Natural Science Fund of Inner Mongolia Autonomous Region (2017MS0107,2018MS01020,2019BS01010),CaoYuanYingCai Projection of Inner Mongolia,Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Regions (NJYT-17-A07) （11761053）
