Error Analysis of a Stochastic Collocation Method for Parabolic Partial Differential Equations with Random Input Data

SIAM Journal on Numerical Analysis ◽

10.1137/11084306x ◽

2012 ◽

Vol 50 (4) ◽

pp. 1922-1940 ◽

Author(s):

Guannan Zhang ◽

Max Gunzburger

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Analysis ◽

Collocation Method ◽

Parabolic Partial Differential Equations ◽

Stochastic Collocation ◽

Random Input ◽

Stochastic Collocation Method ◽

Random Input Data

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A MULTI-FIDELITY STOCHASTIC COLLOCATION METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA

International Journal for Uncertainty Quantification ◽

10.1615/int.j.uncertaintyquantification.2014007778 ◽

2014 ◽

Vol 4 (3) ◽

pp. 225-242 ◽

Author(s):

Maziar Raissi ◽

Padmanabhan Seshaiyer

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Parabolic Partial Differential Equations ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

SIAM Journal on Numerical Analysis ◽

10.1137/050645142 ◽

2007 ◽

Vol 45 (3) ◽

pp. 1005-1034 ◽

Author(s):

Ivo Babuška ◽

Fabio Nobile ◽

Raúl Tempone

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Elliptic Partial Differential Equations ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

SIAM Review ◽

10.1137/100786356 ◽

2010 ◽

Vol 52 (2) ◽

pp. 317-355 ◽

Author(s):

Ivo Babuška ◽

Fabio Nobile ◽

Raúl Tempone

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Elliptic Partial Differential Equations ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Partial Differential Equations with Random Input Data

Lecture Notes in Computational Science and Engineering - Sparse Grids and Applications - Munich 2012 ◽

10.1007/978-3-319-04537-5_6 ◽

2014 ◽

pp. 137-170 ◽

Author(s):

Max Gunzburger ◽

Clayton G. Webster ◽

Guannan Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Adaptive Wavelet ◽

Stochastic Collocation Method ◽

Random Input Data

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A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/140969002 ◽

2015 ◽

Vol 3 (1) ◽

pp. 1046-1074 ◽

Author(s):

A. L. Teckentrup ◽

P. Jantsch ◽

C. G. Webster ◽

M. Gunzburger

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

SIAM Journal on Numerical Analysis ◽

10.1137/070680540 ◽

2008 ◽

Vol 46 (5) ◽

pp. 2411-2442 ◽

Author(s):

F. Nobile ◽

R. Tempone ◽

C. G. Webster

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Sparse Grid ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data.

10.2172/934852 ◽

2007 ◽

Author(s):

Clayton Webster ◽

Raul Tempone ◽

Fabio Nobile

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

High Dimensional ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

SIAM Journal on Numerical Analysis ◽

10.1137/060663660 ◽

2008 ◽

Vol 46 (5) ◽

pp. 2309-2345 ◽

Author(s):

F. Nobile ◽

R. Tempone ◽

C. G. Webster

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Sparse Grid ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Method ◽

Random Input Data

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Accelerating Stochastic Collocation Methods for Partial Differential Equations with Random Input Data

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/15m1019568 ◽

2016 ◽

Vol 4 (1) ◽

pp. 1111-1137 ◽

Author(s):

D. Galindo ◽

P. Jantsch ◽

C. G. Webster ◽

G. Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Methods ◽

Stochastic Collocation ◽

Random Input ◽

Partial Differential ◽

Stochastic Collocation Methods ◽

Random Input Data

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A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data

10.2172/1649669 ◽

2014 ◽

Author(s):

Hoang Tran ◽

Catalin Trenchea ◽

Clayton Webster

Keyword(s):

Convergence Analysis ◽

Collocation Method ◽

Stokes Equations ◽

Navier Stokes ◽

Stochastic Collocation ◽

Random Input ◽

Navier Stokes Equations ◽

Stochastic Collocation Method ◽

Random Input Data

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