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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2685659, 6 pages
Research Article

A Two-Level Additive Schwarz Preconditioning Algorithm for the Weak Galerkin Method for the Second-Order Elliptic Equation

Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Received 16 December 2015; Accepted 9 March 2016

Academic Editor: Yann Favennec

Copyright © 2016 Fangfang Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a two-level additive Schwarz preconditioning algorithm for the weak Galerkin approximation of the second-order elliptic equation. In the algorithm, a conforming finite element space is defined on the coarse mesh, and a stable intergrid transfer operator is proposed to exchange the information between the spaces on the coarse mesh and the fine mesh. With the framework of the Schwarz method, it is proved that the condition number of the preconditioned system only depends on the rate of the coarse mesh size and the overlapping size. Some numerical experiments are carried out to verify the theoretical results.