The characteristic finite volume element method for the nonlinear convection-dominated diffusion problem
The characteristic finite volume element method for the nonlinear convection-dominated diffusion problem
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DOI：
10.1016/j.camwa.2007.11.033
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发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Fuzheng Gao;Yirang Yuan
中科院分区：
文献类型：
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作者：
Fuzheng Gao;Yirang Yuan
在现代油气资源勘探开发数值模拟和环境科学中，考虑非线性对流占优扩散问题的数值方法是非常重要的。针对大型科学工程计算的三维特性等实际情况，提出了一种具有特征的有限体积元方法。采用了变分、交换算子、先验估计理论和技巧等技术。给出了L2范数的次最优阶误差估计和H1范数的最优阶误差估计，以确定近似解的误差。数值结果验证了该方案的性能。
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 L2norm and optimal order error estimate in H1norm are derived to determine the errors for the approximate solution. Numerical results are presented to verify the performance of the scheme.