标题：The characteristic finite volume element method for the nonlinear convection-dominated diffusion problem
作者：Fuzheng Gao;Yirang Yuan
作者机构：[Gao, F] School of Mathematics and System Science, Shandong University, Jinan, 250100 Shandong, China;[ Yuan, Y] School of Mathematics and System Scie 更多
通讯作者地址：[Gao, FZ]Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China.
来源：Computers & Mathematics with Applications: An International Journal
关键词：Nonlinear;Convection-dominated diffusion;Characteristic finite volume element;Error estimate;Numerical experiment
摘要：In modern numerical simulation of prospecting and exploiting oil–gas resources and environmental science, it is important to consider a numerical method for nonlinear convection-dominated diffusion problems. Based on actual conditions, such as the three-dimensional characteristics of large-scale science-engineering computation, we present a kind of characteristic finite volume element method. Some techniques, such as calculus of variations, commutating operators, the theory of prior estimates and techniques, are adopted. Suboptimal order error estimate in L2 norm and optimal order error estimate in H1 norm are derived to determine the errors for the approximate solution. Numerical results are presented to verify the performance of the scheme.