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. © 2014 Elsevier B.V.
Stabilized reduced basis method for parametrized advection-diffusion PDEs
Rozza, Gianluigi
2014-01-01
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. © 2014 Elsevier B.V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
