Adaptive reduced basis strategy dedicated to the solution of nonstationary stochastic thermal problems

Abstract

This contribution addresses the modeling and the stochastic analysis of transient thermal processes by means of the finite element method. It focuses on the theoretical presentation as well as the application of an efficient reduced basis strategy that advantageously lowers the dimension of the investigated system. The modal content of the reduced basis is driven by the goal oriented error assessment of a user-defined quantity of interest. The first section of the article presents the stochastic system of interest: key aspects of a stochastic analysis are recalled along with the employed spatial discretization. The newly developed adaptive reduced basis strategy is then detailed in the second section before extensive numerical investigations are carried out in order to validate it in the last section of the article. A numerical benchmark allowing for the confrontation of the proposed strategy with usual Monte-Carlo simulations highlights the benefits of the method that allows for a precise control of the maximum admissible error on the quantity of interest.