Extension of dual analysis to 3-D problems: evaluation of its advantages in error estimation

The dual analysis is one of the first methods developed to evaluate the discretization error of the finite elements computations. It is based on the comparison of two solutions of a given finite element problem, one of them being of the classical displacement type, the second being of the equilibrium type. This method has proved its efficiency in the frame of elastostatic computations for which it leads to an upper bound of the global error in energy norm. Due to the use of a stiffness matrix, this method is very easy to implement in a standard finite element program and it is computationally very efficient.