Mathematical and numerical results on the parametric sensitivity of a ROM-POD of the Burgers equation

Abstract

We are interested in the mathematical study of the sensitivity of a reduced order model (ROM) of a particular single-parameterised quasi-linear equation, via the parametric evolution. More precisely, the ROM of interest is obtained in two different ways: First, we reduce the complete parametric equation using a proper orthogonal decomposition (POD) basis computed at a given reference value of the parameter, and second the parametric ROM is obtained by an expanded POD basis associated this time to a reference solution and its parametric derivative. The second case of our study was considered in a nearly similar way in Ito and Ravindran (1998), but in the context of the reduced basis (RB) method of the Navier–Stokes equations reduction. Indeed, the authors, Ito and Ravindran (1998) proposed to use an expanded set of basis functions, including solution flows for different values of the Reynolds number and their associated first-order derivatives with respect to this parameter. Beside this work, our second st...