Cascadic Multigrid Method for Isoparametric Finite Element with Numerical Integration

Abstract

The purpose of this paper is to study the cascadic multigrid method for the second-order elliptic problems with curved boundary in two-dimension which are discretized by the isoparametric finite element method with numerical integration. We show that the CCG method is accurate with optimal complexity and traditional multigrid smoother (like symmetric Gauss-Seidel, SSOR or damped Jacobi iteration) is accurate with suboptimal complexity.