Analisi a posteriori dell'errore per il problema di Galerkin Discontinuo per un problema di convezione-reazione

In many cases PDEs can not be directly solved, and an approximated solution is the best which one can find. There is a wide variety of numerical methods for PDEs. In the thesis is presented one of such methods: the Discontinuous Galerkin method. This instance of the method is designed for the case of a general convection-reaction problem, in which a small diffusion term is also admitted. After the description of the problem the thesis proceeds to describe two a-posteriori error estimator. They are quantities which depend on the approximated solution (and which are therefore explicitly computable), and which act as upper bounds for the error of approximation.