The Galerkin method is applied in the non-linear stochastic diffusion problem. The uncertainty is present in the coefficients of diffusion equation. The uncertainty is modeled by random variables. The chaos polynomials is used to approximate the stochastic behavior of the problem. The approximate solutions obtained through Galerkin method are compared with Monte Carlo simulation in terms of the statistical moments of random variables generated by the random field solution.
The numerical simulation is widely used, in now days, to verify the viability and to optimize structural mechanic designs. The numerical approach of elastoplastic materials can found some problems related to ill-conditioning of matrices (from FEM systems), associated to the critical points from the snap through or snap back shape of the equilibrium curve. Aiming to overcome this misfortune it is proposed a strategy via Tikhonov regularization method in association with L-curve technique to determine the regularization parameter. This strategy can be used in many numerical applications for structural analysis. The theoretical development about these Some numerical examples are presented to attest the efficiency of this proposed approach.
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