A NATURAL NORM FOR THE CHARACTERISTIC MET HOD WITH DISCONTINUOUS FINITE-ELEMENTS - CASE 1-D

We consider for the one dimensional steady transport equation the char acteristic method with a pseudo time step k. The unknown is approximat ed by P-r discontinuous finite elements on mesh J(h). For this method, we exhibit a ''natural'' norm parallel to parallel to(h,k) for wich w e show that the discrete variational problem P-h(k) is well posed and we give an error estimate. We show that when k goes to zero problem (P -h(k)) (resp. the parallel to parallel to(h,k) norm) has as a limit pr oblem (P-h) (resp. the parallel to parallel to(h) norm) associated to the Galerkin discontinuous method.