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Mathematical Problems in Engineering
Volume 2016, Article ID 2685659, 6 pages
http://dx.doi.org/10.1155/2016/2685659
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.

Linked References

  1. J. Wang and X. Ye, “A weak Galerkin finite element method for second-order elliptic problems,” Journal of Computational and Applied Mathematics, vol. 241, pp. 103–115, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. R. Zhang and Q. Zhai, “A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order,” Journal of Scientific Computing, vol. 64, no. 2, pp. 559–585, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. V. Ginting, G. Lin, and J. Liu, “On application of the weak Galerkin finite element method to a two-phase model for subsurface flow,” Journal of Scientific Computing, vol. 66, no. 1, pp. 225–239, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  4. L. Chen, J. Wang, and X. Ye, “A posteriori error estimates for weak Galerkin finite element methods for second order elliptic problems,” Journal of Scientific Computing, vol. 59, no. 2, pp. 496–511, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. B. Li and X. Xie, “A two-level algorithm for the weak Galerkin discretization of diffusion problems,” Journal of Computational and Applied Mathematics, vol. 287, pp. 179–195, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. L. Chen, J. Wang, Y. Wang, and X. Ye, “An auxiliary space multigrid preconditioner for the weak Galerkin method,” Computers & Mathematics with Applications, vol. 70, no. 4, pp. 330–344, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. Toselli and O. Widlund, Domain Decomposition Methods Algorithms and Theory, Springer, New York, NY, USA, 2005.
  8. L. Wang and X. Xu, The Mathematical Basis of the Finite Element Method, Science Press, Beijing, China, 2005 (Chinese).
  9. S. Brenner and L. Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, NY, USA, 2008.