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References (25)
-
W. Gautschi (1982)
On Generating Orthogonal PolynomialsSiam Journal on Scientific and Statistical Computing, 3
-
R. Ghanem, P. Spanos (1990)
Stochastic Finite Elements: A Spectral Approach -
L. Mathelin, M. Hussaini (2003)
A Stochastic Collocation Algorithm for Uncertainty Analysis -
R. Abgrall, P. Congedo, C. Corre, S. Galera (2010)
A simple semi-intrusive method for Uncertainty Quantification of shocked flows, comparison with a non-intrusive Polynomial Chaos method -
R. Abgrall (2008)
A simple, flexible and generic deterministic approach to uncertainty quantifications in non linear problems: application to fluid flow problems -
I. Babuska, F. Nobile, R. Tempone (2007)
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input DataSIAM J. Numer. Anal., 45
-
X. Wan, G. Karniadakis (2006)
Long-Term Behavior of Polynomial Chaos in Stochastic Flow SimulationsComputer Methods in Applied Mechanics and Engineering, 195
-
G. Migliorati, F. Nobile, E. Schwerin, R. Tempone (2013)
Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete L2 Projection on Polynomial SpacesSIAM J. Sci. Comput., 35
-
A. Doostan, H. Owhadi (2010)
A non-adapted sparse approximation of PDEs with stochastic inputsJ. Comput. Phys., 230
-
M. Berveiller, B. Sudret, M. Lemaire (2006)
Stochastic finite element: a non intrusive approach by regressionEuropean Journal of Computational Mechanics, 15
-
B. Ganapathysubramanian, N. Zabaras (2007)
Sparse grid collocation schemes for stochastic natural convection problemsJ. Comput. Phys., 225
-
X. Wan, G. Karniadakis (2006)
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability MeasuresSIAM J. Sci. Comput., 28
-
D. Xiu (2010)
Numerical Methods for Stochastic Computations: A Spectral Method Approach -
X. Wan, G. Karniadakis (2005)
An adaptive multi-element generalized polynomial chaos method for stochastic differential equationsJournal of Computational Physics, 209
-
T. Zang, L. Mathelin, M. Hussaini, F. Bataille (2003)
Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods -
M. Reagan, H. Najm, R. Ghanem, O. Knio (2003)
Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projectionCombustion and Flame, 132
-
(2007)
Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables -
D. Xiu (2007)
Efficient collocational approach for parametric uncertainty analysisCommunications in Computational Physics, 2
-
Joakim Beck, F. Nobile, L. Tamellini, R. Tempone (2011)
Implementation of optimal Galerkin and collocation approximations of PDEs with random coefficientsEsaim: Proceedings, 33
-
H. Elman, Christopher Miller, E. Phipps, R. Tuminaro (2011)
ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATAInternational Journal for Uncertainty Quantification, 1
-
Andreas Keese, H. Matthies (2003)
Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations -
D. Xiu, J. Hesthaven (2005)
High-Order Collocation Methods for Differential Equations with Random InputsSIAM J. Sci. Comput., 27
-
C. Clenshaw, A. Curtis (1960)
A method for numerical integration on an automatic computerNumerische Mathematik, 2
-
G. Golub, John Welsch (1967)
Calculation of Gauss quadrature rules -
Géraud Blatman, B. Sudret (2008)
Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approachComptes Rendus Mecanique, 336
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing Switzerland 2015
- ISBN
- 978-3-319-10713-4
- Pages
- 23 –29
- DOI
- 10.1007/978-3-319-10714-1_3
- Publisher site
- See Chapter on Publisher Site
Abstract
[In this chapter we review methods for formulating partial differential equations based on the random field representations outlined in Chap. 2 These include the stochastic Galerkin method, which is the predominant choice in this book, as well as other methods that frequently occur in the literature, e.g., stochastic collocation methods and spectral projection. We also briefly discuss methods that are not polynomial chaos methods themselves but are viable alternatives.]
Published: Sep 17, 2014
Keywords: Quadrature Point; Spectral Projection; Polynomial Chaos; Stochastic Collocation; Stochastic Collocation Method