A BDDC algorithm for the Stokes problem with weak Galerkin discretizations
A BDDC algorithm for the Stokes problem with weak Galerkin discretizations
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DOI：
10.1016/j.camwa.2018.04.024
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Xuemin Tu;Bin Wang-
中科院分区：
文献类型：
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作者：
Xuemin Tu;Bin Wang-
约束平衡区域分解（BDDC）方法已成功地应用于求解二阶椭圆和Stokes问题的协调有限元离散所产生的大型稀疏线性代数方程组。本文采用一种新发展起来的弱伽辽金有限元法对Stokes方程进行离散。设计了一种BDDC算法来求解这样得到的线性系统。粗问题选择边缘/面速度界面平均和平均子域压力。分析了BDDC预处理算子的条件数界，得到了与协调有限元法相同的收敛速度。数值实验验证了理论结果。
The BDDC (balancing domain decomposition by constraints) methods have been applied successfully to solve the large sparse linear algebraic systems arising from conforming finite element discretizations of second order elliptic and Stokes problems. In this paper, the Stokes equations are discretized using the weak Galerkin method, a newly developed nonconforming finite element method. A BDDC algorithm is designed to solve the linear system such obtained. Edge/face velocity interface average and mean subdomain pressure are selected for the coarse problem. The condition number bounds of the BDDC preconditioned operator are analyzed, and the same rate of convergence is obtained as for conforming finite element methods. Numerical experiments are conducted to verify the theoretical results.