Adaptive multigrid methods for hybrid finite elements

We consider in this paper the numerical approximation of second order elliptic problems, using adaptive multigrid finite element techniques focusing our attention in numerical methods for the dual problem. First a general result concerning the a-posteriori error estimation of the numerical solution of both primal and dual variables is stated. The relationship between hybrid formulation and non conforming approximation is used to propose and justify an adaptive multigrid algorithm in order that the computational cost be acceptable. Finally a representative numerical example is presented.