Error bounds for POD expansions of parameterized transient temperatures

Abstract

We focus on the convergence analysis of the POD expansion for the parameterized solutionof transient heat equations. The parameter of interest is the conductivity coefficient. We provethat this expansion converges with exponential accuracy, uniformly if the conductivity coeffi-cient remains within a compact set of positive numbers. This convergence result is independentof the regularity of the temperature with respect to the space and time variables. We presentsome numerical experiments to show that a reduced number of modes allows to represent withhigh accuracy the family of solutions corresponding to parameters that lie in the compact setunder study.