-
1
-
-
13844319204
-
Galerkin finite element approximations of stochastic elliptic partial differential equations
-
I. Babuška, R. Tempone and G.E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM J. Numer. Anal. 42 (2004), 800-825.
-
(2004)
SIAM J. Numer. Anal
, vol.42
, pp. 800-825
-
-
Babuška, I.1
Tempone, R.2
Zouraris, G.E.3
-
2
-
-
13844314882
-
Solving elliptic boundary value problems with uncertain coefficients by the finite element method: The stochastic formulation
-
I. Babuška, R. Tempone, G.E. Zouraris, Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. Comput. Methods Appl. Engrg., 194 (2005), 1251-1294.
-
(2005)
Comput. Methods Appl. Engrg
, vol.194
, pp. 1251-1294
-
-
Babuška, I.1
Tempone, R.2
Zouraris, G.E.3
-
4
-
-
0003766476
-
-
Springer-Verlag, New York
-
C. Canuto, M.Y. Hussaini, A. Quateroni and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988.
-
(1988)
Spectral Methods in Fluid Dynamics
-
-
Canuto, C.1
Hussaini, M.Y.2
Quateroni, A.3
Zang, T.A.4
-
5
-
-
33646526516
-
A stochastic analysis of transient two-phase flow in heterogeneous porous media
-
M. Chen, A.A. Keller, D. Zhang, Z. Lu and G.A. Zyvoloski, A stochastic analysis of transient two-phase flow in heterogeneous porous media, Water Resour. Res., 42 (2006), W03425.
-
(2006)
Water Resour. Res
, vol.42
-
-
Chen, M.1
Keller, A.A.2
Zhang, D.3
Lu, Z.4
Zyvoloski, G.A.5
-
6
-
-
14944366975
-
A stochastic analysis of steady state two-phase flow in heterogeneous media
-
M. Chen, D. Zhang, A. Keller and Z. Lu, A stochastic analysis of steady state two-phase flow in heterogeneous media, Water Resour. Res., 41 (2005), W01006.
-
(2005)
Water Resour. Res
, vol.41
-
-
Chen, M.1
Zhang, D.2
Keller, A.3
Lu, Z.4
-
9
-
-
0035964634
-
Solution of stochastic partial differential equations using Galerkin finite element techniques
-
M.K. Deb, I. Babuška. and J.T. Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Comput. Methods Appl. Mech. Engrg., 190 (2001), 6359-6372.
-
(2001)
Comput. Methods Appl. Mech. Engrg
, vol.190
, pp. 6359-6372
-
-
Deb, M.K.1
Babuška, I.2
Oden, J.T.3
-
10
-
-
0032147785
-
Theory and numerical validation
-
An approach to transport in heterogeneous porous media using the truncated temporal moment equations
-
F. Delay, G. Porel and O. Banton, An approach to transport in heterogeneous porous media using the truncated temporal moment equations: Theory and numerical validation, Transport in Porous Media, 32 (1998), 199-232.
-
(1998)
Transport in Porous Media
, vol.32
, pp. 199-232
-
-
Delay, F.1
Porel, G.2
Banton, O.3
-
13
-
-
0035065935
-
Recursive conditional moment equations for advective transport in randomly heterogeneous velocity fields
-
A. Guadagnini and S.P. Neuman, Recursive conditional moment equations for advective transport in randomly heterogeneous velocity fields, Transport in Porous Media, 42 (2001), 37-67.
-
(2001)
Transport in Porous Media
, vol.42
, pp. 37-67
-
-
Guadagnini, A.1
Neuman, S.P.2
-
16
-
-
0003981320
-
-
fourth ed, Springer, Berlin
-
M. Loève, Probability Theory, fourth ed., Springer, Berlin, 1978.
-
(1978)
Probability Theory
-
-
Loève, M.1
-
17
-
-
33745828718
-
Accurate, effective quantification of uncertainty for flow in heterogeneous reservoirs using the KLME approach
-
Z. Lu and D. Zhang, Accurate, effective quantification of uncertainty for flow in heterogeneous reservoirs using the KLME approach, SPE Journal, 12 (2006), 239-247.
-
(2006)
SPE Journal
, vol.12
, pp. 239-247
-
-
Lu, Z.1
Zhang, D.2
-
18
-
-
23944518704
-
Sthochastic approaches to uncertainty quantification in CFD simulations
-
L. Mathelin, M.Y. Hussaini and T.A. Zang, Sthochastic approaches to uncertainty quantification in CFD simulations, Numerical Algorithms, 38 (2005), 209-236.
-
(2005)
Numerical Algorithms
, vol.38
, pp. 209-236
-
-
Mathelin, L.1
Hussaini, M.Y.2
Zang, T.A.3
-
19
-
-
33646573475
-
Proof of the minimality of the number of nodes in the cubature formula for a hypersphere
-
I.P. Mysovskih, Proof of the minimality of the number of nodes in the cubature formula for a hypersphere, USSR Comput. Math. Math. Phys., 6 (1966), 15-27.
-
(1966)
USSR Comput. Math. Math. Phys
, vol.6
, pp. 15-27
-
-
Mysovskih, I.P.1
-
20
-
-
0027456208
-
Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximations
-
S.P. Neuman, Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximations, Water Resour. Res., 29 (1993), 633-646.
-
(1993)
Water Resour. Res
, vol.29
, pp. 633-646
-
-
Neuman, S.P.1
-
22
-
-
0004161838
-
-
second edition, Cambridge Unviersity Press, Cambridge
-
W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (second edition), Cambridge Unviersity Press, Cambridge, 1995.
-
(1995)
Numerical Recipes in C: The Art of Scientific Computing
-
-
Press, W.H.1
Teukolsky, S.A.2
Vetterling, W.T.3
Flannery, B.P.4
-
24
-
-
33746346426
-
Karhunen-Loéve approximation of random fields by generalzied fast multipole methods
-
Ch. Schwab and R.A. Todor, Karhunen-Loéve approximation of random fields by generalzied fast multipole methods, J. Comput. Phys., 217 (2006), 100-122.
-
(2006)
J. Comput. Phys
, vol.217
, pp. 100-122
-
-
Schwab, C.1
Todor, R.A.2
-
25
-
-
0013442905
-
Remarks on the disposition of points in numerical integration formulas
-
A.H. Stroud, Remarks on the disposition of points in numerical integration formulas, Mathematical Tables and Other Aids to Computation, 11 (1957), 257-261.
-
(1957)
Mathematical Tables and Other Aids to Computation
, vol.11
, pp. 257-261
-
-
Stroud, A.H.1
-
26
-
-
0031392891
-
-
M.A. Tatang, W. Pan, R.G. Prinn, G.J. McRae, An efficeint method for parametric uncertainty analysis of numerical geophysical models, J. Geophys. Res., 102 (1997), 925-21, 932.
-
M.A. Tatang, W. Pan, R.G. Prinn, G.J. McRae, An efficeint method for parametric uncertainty analysis of numerical geophysical models, J. Geophys. Res., 102 (1997), 925-21, 932.
-
-
-
-
27
-
-
34047123580
-
Convergence rates of sparse chaos approximations of elliptic problems with stochastic coefficients
-
to appear
-
R.A. Todor and Ch. Schwab, Convergence rates of sparse chaos approximations of elliptic problems with stochastic coefficients, IMA J. Numer. Anal, to appear, 2007.
-
(2007)
IMA J. Numer. Anal
-
-
Todor, R.A.1
Schwab, C.2
-
28
-
-
33749326978
-
Multi-element generalized polynomial chaos for arbitrary probability measures
-
X. Wan and G. Karniadakis, Multi-element generalized polynomial chaos for arbitrary probability measures, SIAM J. Sci. Comput. 28 (2006), 901-928.
-
(2006)
SIAM J. Sci. Comput
, vol.28
, pp. 901-928
-
-
Wan, X.1
Karniadakis, G.2
-
29
-
-
34447270699
-
Efficient collocational approach for parametric uncertainty analysis
-
D. Xiu, Efficient collocational approach for parametric uncertainty analysis, Commun. Comput. Phys., 2 (2007), 293-309.
-
(2007)
Commun. Comput. Phys
, vol.2
, pp. 293-309
-
-
Xiu, D.1
-
30
-
-
33646577797
-
High-order collocation methods for differential equations with random inputs
-
D. Xiu and J.S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., 27 (2005), 1118-1139.
-
(2005)
SIAM J. Sci. Comput
, vol.27
, pp. 1118-1139
-
-
Xiu, D.1
Hesthaven, J.S.2
-
31
-
-
0037184252
-
Modeling undertainty in steady state diffusion problems via generalized polynomial chaos
-
D. Xiu and G.E. Karniadakis, Modeling undertainty in steady state diffusion problems via generalized polynomial chaos, Comput. Methods Appl. Mech. Eng., 191 (2002), 4927-4948.
-
(2002)
Comput. Methods Appl. Mech. Eng
, vol.191
, pp. 4927-4948
-
-
Xiu, D.1
Karniadakis, G.E.2
-
32
-
-
0037249229
-
The Wiener-Askey polynomial chaos for stochastic differential equations
-
D. Xiu and G.E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), 619-644.
-
(2002)
SIAM J. Sci. Comput
, vol.24
, pp. 619-644
-
-
Xiu, D.1
Karniadakis, G.E.2
-
33
-
-
0037408312
-
Modeling uncertainty in flow simulations via generalized polynomial chaos
-
D. Xiu and G.E. Karniadakis, Modeling uncertainty in flow simulations via generalized polynomial chaos, J. Comput. Phys., 187 (2003), 137-167.
-
(2003)
J. Comput. Phys
, vol.187
, pp. 137-167
-
-
Xiu, D.1
Karniadakis, G.E.2
-
34
-
-
34147178547
-
An efficient spectral method for acoustic scattering from rough surfaces
-
D. Xiu and J. Shen, An efficient spectral method for acoustic scattering from rough surfaces, Commun. Comput. Phys., 2 (2007), 54-72.
-
(2007)
Commun. Comput. Phys
, vol.2
, pp. 54-72
-
-
Xiu, D.1
Shen, J.2
-
35
-
-
3042595850
-
Stochastic analysis of saturated-unsaturated flow in heterogeneous media by combining Karhunen-Loève expansion and perturbation method
-
J. Yang, D. Zhang and Z. Lu, Stochastic analysis of saturated-unsaturated flow in heterogeneous media by combining Karhunen-Loève expansion and perturbation method, J. Hydrology, 294 (2004), 18-38.
-
(2004)
J. Hydrology
, vol.294
, pp. 18-38
-
-
Yang, J.1
Zhang, D.2
Lu, Z.3
-
36
-
-
0032634748
-
Nonstationary stochastic analysis of transient unsaturated flow in randomly heterogeneous media
-
D. Zhang, Nonstationary stochastic analysis of transient unsaturated flow in randomly heterogeneous media, Water Resour. Res., 35 (1999), 1127-1141.
-
(1999)
Water Resour. Res
, vol.35
, pp. 1127-1141
-
-
Zhang, D.1
-
37
-
-
50049125230
-
-
D. Zhang, Stochastic Methods for Flow in Porous Media: Coping With Uncertainties, Academic Press, San Diego, 2002.
-
D. Zhang, Stochastic Methods for Flow in Porous Media: Coping With Uncertainties, Academic Press, San Diego, 2002.
-
-
-
-
38
-
-
1442307688
-
An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions
-
D. Zhang and Z. Lu, An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions, J. Comput. Phys., 194 (2003), 773-794.
-
(2003)
J. Comput. Phys
, vol.194
, pp. 773-794
-
-
Zhang, D.1
Lu, Z.2
|