Integral boundary conditions in F.E.M approaches with the minimization of constitutive error

A method based on the minimization of the constitutive error has been successfully applied to finite element formulations of Maxwell equations. Error based techniques present a number of appealing characteristics, including the possibility of providing an estimation of the error distribution and to split the equation system in two decoupled subsystems. However, except for very simple cases, a direct numerical translation of the boundary conditions can cause a number of drawbacks: on one side the lack of symmetry and positive definition of the matrix, on the other side the impossibility of splitting the unknowns. This paper is aiming to discuss the problem and to propose a technique to effectively impose a wide class of boundary conditions within the framework of error based formulations. To show the performance of the technique, some examples are proposed.