The current work concerns the study and the implementation of a modern algorithm for error estimation in CFD computations. This estimate involves the dealing of the adjoint argument. By solving the adjoint problem, it is possible to obtain important information about the transport of the error towards the quantity of interest. The aim is to apply for the first time this procedure into Petrov-Galerkin (PG) method. Streamline Upwind Petrov-Galerkin, stabilised Residual Distribution and bubble method are involved for the implementation. Scalar hyperbolic problems are firstly used as test cases.