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Stochastic Finite Elements

Maurice Lemaire · Alaa Chateauneuf · Jean‐Claude Mitteau

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Probabilistic and Robust Engineering Design Advanced Numerical Methods in Computational Mathematics Geotechnical Engineering and Analysis

Abstract

This chapter contains sections titled: Introduction Spatial discretization of a random field Series expansion of a random field Finite element method and gradient calculation Perturbation method Polynomial chaos expansion Continuous random field methods An illustration Conclusion

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References

2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 1987Stochastic Differential Equations: An Introduction with Applications.2017Structural Reliability Analysis and Prediction 2006An introduction to stochastic partial differential equations 1954ON STATIONARY PROCESSES IN THE PLANE 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 1997Stochastic Analysis 2008The stochastic finite element method: Past, present and future

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