本文選題：二階橢圓問題　切入點：弱Galerkin方法　出處：《南京師范大學》2015年碩士論文

【摘要】：本文提出了一種求解二階橢圓問題弱Galerkin方法的兩水平加性Schwarz預處理算法.論文首先介紹了二階橢圓問題的弱Galerkin離散方法,并給出了離散逼近誤差；其次引入了一種弱Galerkin離散方法的兩水平加性Schwarz預條件子,給出了一種網(wǎng)格轉移算子,證明了其穩(wěn)定性和逼近性；接著估計了預處理后的弱Galerkin離散算子的最大特征值和最小特征值,給出了預處理算子的條件數(shù)上界；最后我們通過數(shù)值試驗驗證了理論結果.
[Abstract]:In this paper, a two-level additive Schwarz preprocessing algorithm for weak Galerkin method for second-order elliptic problems is proposed.In this paper, the weak Galerkin discretization method for the second order elliptic problem is introduced, and the discrete approximation error is given. Secondly, a two-level additive Schwarz preconditioner of a weak Galerkin discrete method is introduced, and a mesh transfer operator is given.The stability and approximation are proved, and then the maximum and minimum eigenvalues of the pretreated weak Galerkin discrete operator are estimated, and the upper bound of the condition number of the preprocessing operator is given. Finally, the theoretical results are verified by numerical experiments.
【學位授予單位】：南京師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O241.82

【參考文獻】

相關期刊論文 前1條

1 ;A COARSENING ALGORITHM ON ADAPTIVE GRIDS BY NEWEST VERTEX BISECTION AND ITS APPLICATIONS[J];Journal of Computational Mathematics;2010年06期

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本文編號：1703333