【摘要】：有限體積元方法格式構造簡單,并且能保持數值流量的局部守恒性,因此在計算流體力學、電磁場等領域有著廣泛的應用.本文主要分為兩部分,第一部分研究對流擴散反應問題基于Crouzeix-Raviart非協(xié)調元的迎風有限體積元方法的逼近誤差在1范數意義下的后驗誤差估計,借助對流擴散反應問題基于協(xié)調元的具有迎風格式和基于非協(xié)調元的不具迎風格式的有限體積元方法的后驗誤差估計的方法,運用迎風格式處理對流項,最后得到了逼近誤差在1范數意義下的后驗誤差估計整體上界.第二部分研究了單調非線性橢圓問題基于Crouzeix-Raviart非協(xié)調元的有限體積元方法,得到了逼近誤差先驗估計,以及在1和2范數意義下的后驗誤差估計子.
[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.
【學位授予單位】：煙臺大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.8

【參考文獻】

相關期刊論文 前1條

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

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本文編號：2410599