Application of Least-Squares Spectral Element Methods to Polynomial Chaos

Conference object English OPEN
Vos, P.E.J.; Gerritsma, M.I.;
(2006)
  • Publisher: Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)
  • Subject: spectral elements | least squares | stochastic differential equations | polynomial chaos

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conv... View more
  • References (18)
    18 references, page 1 of 2

    [1] D. Xiu and G.E. Karniadakis, Modeling uncertainty in ow simulations via generalized polynomial chaos, J. Comput. Phys., Vol. 187, Issue 1, 137-167, (2003).

    [2] D. Xiu and G.E. Karniadakis, Wiener-Askey polynomial chaos for stochastic di erential equations, SIAM J. Sci. Comput., Vol 24(2), 619-644, (2002).

    [3] B.-N. Jiang, The Least-Squares Finite Element Method, Springer, Berlin Heidelberg, Germany, (1998).

    [4] M.M.J. Proot,The Least-Squares Spectral Element Method, Ph.D. thesis, Delft University of Technology, Department of Aerospace Engineering, Delft, The Netherlands, (2003).

    [5] R.G. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York, USA, (1991).

    [6] N. Wiener, The Homogeneous Chaos, Amer. J. Math., 60, 897-936, (2003).

    [7] R. Koekoek and R. Swarttouw,The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Tech. Report 98-17, Delft University of Technology, Department of Technical Mathematics and Informatics, Delft, The Netherlands, (1998).

    [8] X. Wan and G.E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochasti di erential equations, J. Comput. Phys., Vol. 209, Issue 2, 617-642, (2005).

    [9] O.P. Le Maitre, H.N. Njam, R.G. Ghanem and O.M. Knio,Uncertainty propagation using Wiener-Haar expansions, J. Comput. Phys., Vol. 197, Issue 1, 28-57, (2004).

    [10] A.M. Mood, F.A. Graybill and D.C. Boes, Introduction to the Theory of Statistics, 3rd Ed., McGraw-Hill, (1950).

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