本文選題：對流擴散特征征值問題 + Crouzeix-Raviart非協(xié)調(diào)元�。� 參考：《貴州師范大學》2017年碩士論文

【摘要】：對流擴散特征值問題在流體力學和能源科學等多個領域都有廣泛應用,也因此成為了學者關注的熱點問題.過去研究對流擴散特征值問題的后驗誤差估計多是采用協(xié)調(diào)有限元方法,而本文則首次研究了求解對流擴散特征值問題的Crouzeix-Raviart非協(xié)調(diào)元自適應算法,文章給出了相應的后驗誤差估計,并證明了后驗誤差指示子的可靠性和有效性.根據(jù)本文的后驗誤差估計,我們在數(shù)值實驗中建立了Crouzeix-Raviart元自適應算法來求解對流擴散特征值問題,并基于Xu和Zhou提出的二網(wǎng)格方法給出了一個用Crouzeix-Raviart元求解對流擴散特征值問題的二網(wǎng)格離散方案.得到的數(shù)值結果驗證了我們的理論分析,并且也表明本文建立的自適應算法和二網(wǎng)格離散方案都是高效的.且與一致網(wǎng)格加密相比帶有自適應加密的二網(wǎng)格離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.
【學位授予單位】：貴州師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.82

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相關期刊論文 前2條

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本文編號：2040331