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Mathematical Problems in Engineering
Volume 2017, Article ID 7912845, 8 pages
https://doi.org/10.1155/2017/7912845
Research Article

The Cascadic Multigrid Method of the Weak Galerkin Method for Second-Order Elliptic Equation

1School of Mathematical Sciences, Tongji University, Shanghai 200092, China
2School of Mathematical and Statistics, Xinyang Normal University, Xinyang 464000, China

Correspondence should be addressed to Cheng Wang; nc.ude.ijgnot@gnehcgnaw

Received 28 April 2017; Accepted 17 September 2017; Published 18 October 2017

Academic Editor: Petr Krysl

Copyright © 2017 Shi Sun 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.

Abstract

This paper is devoted to the analysis of the cascadic multigrid algorithm for solving the linear system arising from the weak Galerkin finite element method. The proposed cascadic multigrid method is optimal for conjugate gradient iteration and quasi-optimal for Jacobi, Gauss-Seidel, and Richardson iterations. Numerical results are also provided to validate our theoretical analysis.