基于Crouzeix-Raviart元的有限体积元方法的误差估计
发布时间：2019-01-18 10:07
【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,因此在计算流体力学、电磁场等领域有着广泛的应用.本文主要分为两部分,第一部分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1范数意义下的后验误差估计,借助对流扩散反应问题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的方法,运用迎风格式处理对流项,最后得到了逼近误差在1范数意义下的后验误差估计整体上界.第二部分研究了单调非线性椭圆问题基于Crouzeix-Raviart非协调元的有限体积元方法,得到了逼近误差先验估计,以及在1和2范数意义下的后验误差估计子.
[Abstract]:The finite volume element method (FVM) is simple in structure and can maintain the local conservation of numerical flow, so it is widely used in computational fluid dynamics, electromagnetic field and other fields. This paper is mainly divided into two parts. In the first part, the posteriori error estimation of upwind finite volume element method based on Crouzeix-Raviart nonconforming element is studied in the sense of 1 norm. The upwind scheme is used to deal with the convection term by means of the posteriori error estimation method of the convection-diffusion reaction problem based on the upwind scheme with the conforming element and the finite volume element method without the upwind scheme based on the nonconforming element. Finally, the global upper bound of the posteriori error estimation for approximation error in the sense of 1 norm is obtained. In the second part, the finite volume element method based on Crouzeix-Raviart nonconforming element for monotone nonlinear elliptic problems is studied. A priori estimate of approximation error and a posteriori error estimator in the sense of 1 and 2 norms are obtained.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
本文编号：2410599
[Abstract]:The finite volume element method (FVM) is simple in structure and can maintain the local conservation of numerical flow, so it is widely used in computational fluid dynamics, electromagnetic field and other fields. This paper is mainly divided into two parts. In the first part, the posteriori error estimation of upwind finite volume element method based on Crouzeix-Raviart nonconforming element is studied in the sense of 1 norm. The upwind scheme is used to deal with the convection term by means of the posteriori error estimation method of the convection-diffusion reaction problem based on the upwind scheme with the conforming element and the finite volume element method without the upwind scheme based on the nonconforming element. Finally, the global upper bound of the posteriori error estimation for approximation error in the sense of 1 norm is obtained. In the second part, the finite volume element method based on Crouzeix-Raviart nonconforming element for monotone nonlinear elliptic problems is studied. A priori estimate of approximation error and a posteriori error estimator in the sense of 1 and 2 norms are obtained.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
【参考文献】
相关期刊论文 前1条
1 HU Jun;MA Rui1;SHI ZhongCi;;A new a priori error estimate of nonconforming finite element methods[J];Science China(Mathematics);2014年05期
，本文编号：2410599
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