【摘要】：有限體積元方法格式構(gòu)造簡(jiǎn)單,并且能保持?jǐn)?shù)值流量的局部守恒性,因此在計(jì)算流體力學(xué)、電磁場(chǎng)等領(lǐng)域有著廣泛的應(yīng)用.本文主要分為兩部分,第一部分研究對(duì)流擴(kuò)散反應(yīng)問題基于Crouzeix-Raviart非協(xié)調(diào)元的迎風(fēng)有限體積元方法的逼近誤差在1范數(shù)意義下的后驗(yàn)誤差估計(jì),借助對(duì)流擴(kuò)散反應(yīng)問題基于協(xié)調(diào)元的具有迎風(fēng)格式和基于非協(xié)調(diào)元的不具迎風(fēng)格式的有限體積元方法的后驗(yàn)誤差估計(jì)的方法,運(yùn)用迎風(fēng)格式處理對(duì)流項(xiàng),最后得到了逼近誤差在1范數(shù)意義下的后驗(yàn)誤差估計(jì)整體上界.第二部分研究了單調(diào)非線性橢圓問題基于Crouzeix-Raviart非協(xié)調(diào)元的有限體積元方法,得到了逼近誤差先驗(yàn)估計(jì),以及在1和2范數(shù)意義下的后驗(yàn)誤差估計(jì)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(xué)位授予單位】：煙臺(tái)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8

【參考文獻(xiàn)】

相關(guān)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(hào)：2410599