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对流扩散反应问题的迎风有限体积元方法的后验误差估计

发表时间:2017-04-14  浏览量:1323  下载量:139
全部作者: 刘晓,毕春加
作者单位: 烟台大学数学与信息科学学院
摘 要: 有限体积元方法格式构造简单,并且能保持数值流量的局部守恒性。研究对流扩散反应问题基于Crouzeix-Raviart非协调元的迎风有限体积元方法的逼近误差在H1范数意义下的后验误差估计,主要参考对流扩散反应方程基于协调元的具有迎风格式和基于非协调元的不具迎风格式的有限体积元方法的后验误差估计方法,运用迎风格式处理对流项,得到了逼近误差在H1范数意义下的后验误差估计整体上界。
关 键 词: 计算数学;对流扩散反应方程;有限体积元方法;Crouzeix-Raviart非协调元;后验误差估计
Title: A posteriori error estimate of finite volume elements method with upwind scheme for convection-diffusion-reaction problem
Author: LIU Xiao, BI Chunjia
Organization: School of Mathematics and Information Sciences, Yantai University
Abstract: The finite volume element structure is simple, and it keeps the local conservativeness of the numerical flow. The main purpose of this paper is to give posteriori H1 error estimate for Crouzeix-Raviart nonconforming finite volume element method with upwind scheme for convection-diffusion-reaction problem. The main reference is the calculation method of the upwind scheme based on the conforming finite element and the scheme without upwind based on Crouzeix-Raviart nonconforming finite volume element. Using the upwind scheme to treat the convection term, finally, we get the global upper bound of the posteriori error estimator in the H1 norm.
Key words: computational mathematics; convection-diffusion-reaction equations; finite volume element method; Crouzeix-Raviart nonconforming element; posteriori error estimate
发表期数: 2017年4月第7期
引用格式: 刘晓,毕春加. 对流扩散反应问题的迎风有限体积元方法的后验误差估计[J]. 中国科技论文在线精品论文,2017,10(7):709-717.
 
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