Error estimation based on a new principle of projection and reconstruction

A new approach for error estimation in finite element computations is presented. This method may be applied to a wide range of modeling (magnetostatics, magnetodynamics, scattering problems). The main idea is to reconstruct, from the finite element solution of a primal formulation, a field belonging to the space of the dual finite element formulation. The error is then computed through the nonfulfilment of the constitutive relation by the couple: primal solution-dual solution. 2-D problems with analytical solutions are treated to prove the efficiency of the method. Then the error estimator is used to adapt the mesh for a 3-D magnetostatic problem.