A-posteriori error estimation and adaptivity for the finite element methodusing duality principles

The present study introduces the concept of error estimation for locally an d globally defined variables in structural mechanics. As a basic component of the formulation a dual problem specifically designed for the variables i n mind is defined. The influence of the errors of the entire spatial or tem poral domain on the local error of the specific variable is filtered out by the corresponding dual (influence) problem. The duality techniques are reb ated to the principle of Betti-Maxwell and can be used for error estimation with respect to various locally or globally defined variables.