SECOND ORDER MOMENTS OF SOLUTIONS OF PARABOLIC INITIAL BOUNDARY VALUE PROBLEMS WITH ε-CORRELATED RANDOM PARAMETERS

摘要

Due to the random character of input data of a great variety of technical and economical procedures it seems to be appropriate to model these procedures by stochastic initial boundary value problems (IBVP). This paper deals with IBVP for parabolic partial differential equations where a Neumann boundary condition is assumed to be a random field with a given probability distribution. We assume, that this random field possesses smooth paths and that it is homogeneous and short-range correlated with a small correlation length ε > 0. The main interest lies in the calculation of the moment functions of the solution of the considered problem, which depend on the chosen characteristics of the random influence. Based on the idea of an appropriate FEM discretisation we present several approximation procedures for the computation of the variance and correlation function of the discretised solution. Considering a numerical example the resulting variance functions of the introduced methods are compared with the results of a Monte Carlo simulation.