对流扩散特征值问题的Crouzeix-Raviart元自适应方法

发布时间：2018-06-19 15:24

本文选题：对流扩散特征征值问题 + Crouzeix-Raviart非协调元　；参考：《贵州师范大学》2017年硕士论文

【摘要】：对流扩散特征值问题在流体力学和能源科学等多个领域都有广泛应用,也因此成为了学者关注的热点问题.过去研究对流扩散特征值问题的后验误差估计多是采用协调有限元方法,而本文则首次研究了求解对流扩散特征值问题的Crouzeix-Raviart非协调元自适应算法,文章给出了相应的后验误差估计,并证明了后验误差指示子的可靠性和有效性.根据本文的后验误差估计,我们在数值实验中建立了Crouzeix-Raviart元自适应算法来求解对流扩散特征值问题,并基于Xu和Zhou提出的二网格方法给出了一个用Crouzeix-Raviart元求解对流扩散特征值问题的二网格离散方案.得到的数值结果验证了我们的理论分析,并且也表明本文建立的自适应算法和二网格离散方案都是高效的.且与一致网格加密相比带有自适应加密的二网格离散方案得到了精度更高的特征值。
[Abstract]:Convection-diffusion eigenvalue problems have been widely used in many fields such as hydrodynamics and energy science. In the past, most of the posteriori error estimates of convection-diffusion eigenvalue problems were studied by means of concordant finite element method. The Crouzeix-Raviart non-conforming element adaptive algorithm for solving convection-diffusion eigenvalue problems was studied for the first time in this paper. In this paper, a posteriori error estimate is given and the reliability and validity of the posteriori error indicator are proved. A Crouzeix-Raviart element adaptive algorithm is established to solve the convection-diffusion eigenvalue problem in numerical experiments according to the posteriori error estimates in this paper. A two-grid discrete scheme using Crouzeix-Raviart element to solve the convection-diffusion eigenvalue problem is presented based on the two-grid method proposed by Xu and Zhou. The numerical results show that the proposed adaptive algorithm and the two-grid discretization scheme are efficient. Compared with uniform mesh encryption, the two-grid discretization scheme with adaptive encryption has higher accuracy eigenvalues.
【学位授予单位】：贵州师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.82

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