@article {PacciariniRozza2014, title = {Stabilized reduced basis method for parametrized advection-diffusion PDEs}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {274}, year = {2014}, pages = {1{\textendash}18}, 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 {\textquoteleft}{\textquoteleft}double{\textquoteright}{\textquoteright} stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

}, doi = {10.1016/j.cma.2014.02.005}, author = {Pacciarini, P. and Gianluigi Rozza} }