Uncertainty propagation through stochastic elliptic type of partial differential equations are considered. An alternative approach by projecting the solution of the discretized equation into a finite dimensional stochastic vector basis is investigated. It is shown that the solution can be obtained using a reduced series comprising random eigenvalues and eigenvectors of the underlying system matrix. Based on the projection in the stochastic vector basis, a Galerkin error minimization approach is proposed. The constants appearing in the Galerkin method are obtained exactly in closed-form in terms of the random eiegnsolutions. The random eigensolutions in turn are obtained by existing approaches available for the random matrix eigenvalue problems. A hybrid analytical and simulation based computational approach is proposed to obtain the moments and pdf of the solution. The method is illustrated using a stochastic beam problem. The results are compared with the direct Monte Carlo simulation results for different correlation lengths and strengths of randomness.
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