An extended stochastic finite element method for solving stochastic partial differential equations on random domains

Recently, a new strategy was proposed to solve stochastic partial differential equations on random domains. It is based on the extension to the stochastic framework of the extended finite element method (X-FEM). This method leads by a “direct” calculus to an explicit solution in terms of the variabl...

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Bibliographic Details
Published inComputer methods in applied mechanics and engineering Vol. 197; no. 51; pp. 4663 - 4682
Main Authors Nouy, A., Clément, A., Schoefs, F., Moës, N.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 15.10.2008
Elsevier
Subjects
Computational stochastic mechanics
Computational techniques
Engineering Sciences
Exact sciences and technology
Extended finite element method
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Mathematics
Mechanics
Numerical Analysis
Physics
Polynomial chaos
Random domain
Solid mechanics
Stochastic finite element
Stochastic partial differential equations
Structural and continuum mechanics
Structural mechanics
Stochastic partial differential equations
Stochastic finite element
Polynomial chaos
Random domain
Extended finite element method
Computational stochastic mechanics
Chaos
Probabilistic approach
Contour line
Modeling
Orthogonal polynomial
Finite element method
Galerkin method
Deterministic approach
Structural analysis
Stochastic equation
eXtended Finite Element Method
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Summary:Recently, a new strategy was proposed to solve stochastic partial differential equations on random domains. It is based on the extension to the stochastic framework of the extended finite element method (X-FEM). This method leads by a “direct” calculus to an explicit solution in terms of the variables describing the randomness on the geometry. It relies on two major points: the implicit representation of complex geometries using random level-set functions and the use of a Galerkin approximation at both stochastic and deterministic levels. In this article, we detail the basis of this technique, from theoretical and technical points of view. Several numerical examples illustrate the efficiency of this method and compare it to other approaches.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2008.06.010