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

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shi Sun ◽  
Ziping Huang ◽  
Cheng Wang ◽  
Liming Guo
Keyword(s):  
Finite Element Method ◽  
Multigrid Method ◽  
Order Elliptic Equation ◽  
Galerkin Finite Element Method ◽  
Weak Galerkin ◽  
Galerkin Finite Element ◽  
Multigrid Algorithm ◽  
Second Order Elliptic Equation ◽  
Cascadic Multigrid ◽  
Cascadic Multigrid Method

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.

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