The paper presents a view on applications of stochastic finite elements(S.F.E.)⊂ R3 in one complex system, considering a differential equation with random parameters, () Q t g t V d z V y V x k y z k x y k x x y z x y z = ∂ ∂ − ∂ ∂ − ∂ ∂ − ∂ ∂ − ∂ ∂ − ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ ∂ ∂ + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ ∂ ∂ ∂ ∂ + ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ ∂ ∂ φ φ φ φ φ α φ φ φ 2 () () where, x, y, z are the 3D spatial coordinates,. t- the processes time φ =φ (x, y, z,t) is a process function (temperature, pressure etc) Kij- the conductivity tensor.In general case it is: zx zx zz yx yy zz xx xy xz K K K K K K K K K K = (12), d- capacity coefficient (function),g- mass coefficient (function),Q- density of the volume flux, V –velocity vector. This equation in specific conditions goes to: - non stationary fluid flow in porous medium (or / and), - mass transport (or /and) - heat transfer (or/and) - vibrating system etc. The paper contains: 1-An approach of the mean value estimation of the parameter distributions, using S.F.E.. The next is defined as a block vi, with the random function Z(x), where x∈vi. is a random variable i.e. the value at point x determines the respective probability distribution p(x). After the estimation of the mean value over the domain vi, is calculated by zvi = ∫ i v i Z x dx v 1 () (1) 2.-Development of the numerical model using S.F.E. applying a mixed algorithm at the, i.e. it is applied. the Galerkin,s approach not "as a whole" as it is often happened in the literature[3][15], but partly, combining it with other numerical procedure as Runge-Kutta of the fourth order etc. In this treatment, the initial and boundary conditions have been supposed to be treated specifically according by the given problem. 1286 3.- Several simple examples as particular case of the mentioned equation. 4.-Conclusions, the good things of the S.F.E in stationary flow, mass transport, heat transfer, vibrating, subsidence, waving, deformations, consolidations, earthquakes and other phenomenon's.
Some processes are complex, as non stationary flow, mass transport, heat transfer, vibrating, subsidence, waving, deformations, consolidations, earthquakes and other geodynamics, reservoir engineering [1][14][16] Their complexity depend on their random mechanical, physical, chemical etc parameters, relations between them, their risk state etc.. Several processes could be deterministic, other ones stochastic, several could be studded "separately and independently" as the simple heat conduction, one phase fluid flow in porous medium etc.
