Mathematical and numerical results on the sensitivity of the POD approximation relative to the Burgers equation

摘要

From mathematical and numerical points of view, we study the sensitivity with respect to parametric evolutions, of the error obtained by approximating a given parametric partial differential equation using a proper orthogonal decomposition (POD) basis determined once and for all, with association to a fixed parameter. More precisely, we will be considering the one-dimensional Burgers equation with a source term.