二阶椭圆问题弱Galerkin方法的两水平加性Schwarz预处理算法

发布时间：2018-04-03 03:07

本文选题：二阶椭圆问题　切入点：弱Galerkin方法　出处：《南京师范大学》2015年硕士论文

【摘要】：本文提出了一种求解二阶椭圆问题弱Galerkin方法的两水平加性Schwarz预处理算法.论文首先介绍了二阶椭圆问题的弱Galerkin离散方法,并给出了离散逼近误差；其次引入了一种弱Galerkin离散方法的两水平加性Schwarz预条件子,给出了一种网格转移算子,证明了其稳定性和逼近性；接着估计了预处理后的弱Galerkin离散算子的最大特征值和最小特征值,给出了预处理算子的条件数上界；最后我们通过数值试验验证了理论结果.
[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.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.82

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