Error bounds for POD expansions of parameterized transient temperatures

We focus on the convergence analysis of the POD expansion for the parameterized solution of transient heat equations. The parameter of interest is the conductivity coefficient. We prove that this expansion converges with exponential accuracy, uniformly if the conductivity coefficient remains within a compact set of positive numbers. This convergence result is independent of the regularity of the temperature with respect to the space and time variables. We present some numerical experiments to show that a reduced number of modes allows to represent with high accuracy the family of solutions corresponding to parameters that lie in the compact set under study.