Stochastic Solution for non linear problem with Polynomial Chaos method - Καραχάλιος, Δημήτριος (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Χημικών Μηχανικών)
In the deterministic case, the solution of a non linear problem can easily approached by iterative methods. In the case of, that we have to deal with a stochastic non linear problem, the domain does not however, have a physical meaning that permits a sensible discretization. In this context the abstract Hilbert space foundation of the finite element method becomes useful as it can be extended to deal with random functions. In this thesis we intended to solve one nonlinear problem with a random variable with the polynomial chaos expansion method. In a more applied sense, it is sought to describe random processes in such a manner that they can be implemented in a finite element formulation of the physical problem.