Abstract | In this work, we propose viable and efficient strategies for the stabilization of the reduced basis
approximation of an advection dominated problem. In particular, we investigate the combination
of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We
explain why the stabilization is needed in both stages and we identify, analytically and numerically,
which are the drawbacks of a stabilization performed only during the construction of the reduced
basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances
of the double stabilization both in steady and unsteady problems, also related to heat transfer
phenomena. |