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A Two-level Additive Schwarz Preconditioning Algorithm for the Weak Galerkin Method for the Second-order Elliptic Equation
Fangfang Qin 1,Min Zha 2,Feng Wang 2 *
1.Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023
2.Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023
*Correspondence author
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Funding: the Doctoralfund of Ministry of Education of China （No.20123207120001）
Opened online:21 December 2015
Accepted by: none
Citation: Fangfang Qin,Min Zha,Feng Wang.A Two-level Additive Schwarz Preconditioning Algorithm for the Weak Galerkin Method for the Second-order Elliptic Equation[OL]. [21 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4670905
 
 
This paper study a two-level additive Schwarz preconditioning algorithmfor the weak Galerkin approximation of the second-order elliptic equation.In the algorithm, a $P_1$ conforming finite element space is defined on the coarse mesh,and an stable intergrid transfer operator is proposed to exchange the information between the problems on the coarse mesh and the fine mesh.With the framework of the Schwarz method, it is proved that the algorithm is quasi-optimal, that is, the condition number of the preconditioned system only logarithmically depends on the rate of the coarse and fine mesh size.Some numerical experiments are carried out to verify the theoretical results.
Keywords:Computational Mathematics,weak Galerkin, domain decomposition, two-level additive Schwarz preconditioner.
 
 
 

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