Extrapolation cascadic multigrid method on piecewise uniform grid

The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete H 1 -norm and global extrapolation in discrete L 2 -norm are proved. Based on these global estimates the conjugate gradient method (CG) is effective, which is applied to extrapolation cascadic multigrid method (EXCMG). The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient.