High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

Guang Yih Sheu

Department of Accounting and Information System, Chang-Jung Christian University, Gueiren, Tainan, Taiwan.

DOI: 10.4236/am.2013.45A003                

Abstract

This study presents an experiment of improving the performance of spectral stochastic finite element method using high-order elements. This experiment is implemented through a two-dimensional spectral stochastic finite element formulation of an elliptic partial differential equation having stochastic coefficients. Deriving this spectral stochastic finite element formulation couples a two-dimensional deterministic finite element formulation of an elliptic partial differential equation with generalized polynomial chaos expansions of stochastic coefficients. Further inspection of the performance of resulting spectral stochastic finite element formulation with adopting linear and quadratic (9-node or 8-node) quadrilateral elements finds that more accurate standard deviations of unknowns are surprisingly predicted using quadratic quadrilateral elements, especially under high autocorrelation function values of stochastic coefficients. In addition, creating spectral stochastic finite element results using quadratic quadrilateral elements is not unacceptably time-consuming. Therefore, this study concludes that adopting high-order elements can be a lower-cost method to improve the performance of spectral stochastic finite element method.

Keywords

Spectral Stochastic Finite Element Method; Generalized Polynomial Chaos Expansion; High-Order Elements

Conflicts of Interest

The authors declare no conflicts of interest.

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