Stochastic Solution for non linear problem with Polynomial Chaos method [article]

Dimitrios Karachalios, National Technological University Of Athens, National Technological University Of Athens
In the deterministic case, the solution of a nonlinear problem can easily approached by iterative methods. In the case of, that we have to deal with a stochastic nonlinear 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
more » ... able. 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. I would like also to express my gratitude to As. Professor Vissarion Papadopoulo for the assignment of this thesis and Dr. Dimitri Giovani for all explanations and programming implementations.
doi:10.26240/heal.ntua.3810 fatcat:wlt2fgln55bepp6rmuazhqaclm