Abstract

The resource parameter estimation using stochastic finite element, geostatistics etc. is a key point on uncertainty, risk analysis, optimization [1-5] etc. In this view, the paper presents some consideration on: 1) Stochastic finite element estimation. The concept of random element is simplified as a stochastic finite element (SFE) taking into account a parallelepiped element with eight nodes in which are given the probability density functions (pdf) on its point supports. In this context it is shown: a—the stochastic finite element is a linear interpolator, related to the distributions given at each nodes; b—the distribution pdf in whatever point x ∈ V; c—the estimation of the mean value of Z(x); 2) Volume integrals calculus; 3) SFE in geostatistics approaches; 4) SFE in PDE solution. Finally, some conclusions are presented underlying the importance of SFE applications

Highlights

  • IntroductionMany physical phenomena and processes are mathematically modeled by partial differential equations (PDE)

  • The concept of random element is simplified as a stochastic finite element (SFE) taking into account a parallelepiped element with eight nodes in which are given the probability density functions on its point supports

  • In this context it is shown: a—the stochastic finite element is a linear interpolator, related to the distributions given at each nodes; b—the distribution pdf in whatever point x V; c—the estimation of the mean value of Z(x); 2) Volume integrals calculus; 3) SFE in geostatistics approaches; 4) SFE in partial differential equations (PDE) solution

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Summary

Introduction

Many physical phenomena and processes are mathematically modeled by partial differential equations (PDE). The data required by PDE’s models as resource and material parameters are in practice subject to uncertainty due to different errors or modeling assumptions, the lack of knowledge and information. In this view the parameters are (not deterministic) stochastic ones [6]. The considerable attention that stochastic finite element (SFE) received over the last decade [7,8,9] is mainly attributed to the spectacular growth of computing power, rendering possible the efficient treatment of large scale problems in dynamics of processes etc. The geostatistics is a useful discipline to make the inference about the spatial risk phenomenon (processes) [11]

A View on the Random Element
The Mean Value
Variograms
E Z x m x
TVp F in D p g on DD 0
Conclusion

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