Operator weighing in a multigrid method for locally refined grids (Q1905557)

A multigrid method for a second order linear elliptic boundary value problem has been formulated in terms of discretizations of first order equations on all levels. Prolongations and restrictions are introduced separately for scalar and vector fields. Constraints on prolongations and restrictions have been presented, which leads to a very robust multigrid method. It seems that these constraints are necessary conditions for convergence. Some numerical experiments show that operator weighing, as introduced in this paper, improves considerably the rate of convergence.