A V-cycle multigrid for quadrilateral rotated \(Q_1\) element with numerical integration.
A V-cycle multigrid for quadrilateral rotated \(Q_1\) element with numerical integration.
The authors investigate multigrid methods for solving discrete algebraic equations obtained by using the quadrilateral rotated \(Q_1\) elements. An effective V-cycle multigrid algorithm is presented with numerical integrations. A uniform convergence factor is obtained. A similar idea has been exploited for the Wilson nonconforming element [cf. \textit{Z. Shi} and \textit{X. Xu}, Sciences in China, Ser. A 29, 880--891 (1999)] and the TRUNC plate element [cf. \textit{Z. Shi} and \textit{X. Xu}, Comput. Methods Appl. Mech. Eng. 188, 483--493 (2000; Zbl 0963.74065)].
V-cycle multigrid algorithm, Multigrid methods; domain decomposition for boundary value problems involving PDEs, convergence, Boundary value problems for second-order elliptic equations, second-order elliptic problems, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Navier-Stokes equations, rotated \(Q_1\) elements
V-cycle multigrid algorithm, Multigrid methods; domain decomposition for boundary value problems involving PDEs, convergence, Boundary value problems for second-order elliptic equations, second-order elliptic problems, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Navier-Stokes equations, rotated \(Q_1\) elements