Xiu, D.; Sherwin, S. J.; Dong, S.; Karniadakis, G. E. Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows. (English) Zbl 1203.76122 J. Sci. Comput. 25, No. 1-2, 323-346 (2005). MSC: 76M25 65M70 PDFBibTeX XMLCite \textit{D. Xiu} et al., J. Sci. Comput. 25, No. 1--2, 323--346 (2005; Zbl 1203.76122) Full Text: DOI
Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G. Equation-free/Galerkin-free POD-assisted computation of incompressible flows. (English) Zbl 1213.76146 J. Comput. Phys. 207, No. 2, 568-587 (2005). MSC: 76M25 37N10 65M99 PDFBibTeX XMLCite \textit{S. Sirisup} et al., J. Comput. Phys. 207, No. 2, 568--587 (2005; Zbl 1213.76146) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em Supersensitivity due to uncertain boundary conditions. (English) Zbl 1075.76623 Int. J. Numer. Methods Eng. 61, No. 12, 2114-2138 (2004). MSC: 76M22 76M10 76D06 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, Int. J. Numer. Methods Eng. 61, No. 12, 2114--2138 (2004; Zbl 1075.76623) Full Text: DOI
Wan, Xiaoliang; Xiu, Dongbin; Karniadakis, George Em Stochastic solutions for the two-dimensional advection-diffusion equation. (English) Zbl 1075.65010 SIAM J. Sci. Comput. 26, No. 2, 578-590 (2004). MSC: 65C30 65M12 60H15 60H35 65M60 65M70 PDFBibTeX XMLCite \textit{X. Wan} et al., SIAM J. Sci. Comput. 26, No. 2, 578--590 (2004; Zbl 1075.65010) Full Text: DOI
Xiu, Dongbin; Lucor, Didier; Su, C.-H.; Karniadakis, George Em Performance evaluation of generalized polynomial chaos. (English) Zbl 1188.60038 Sloot, Peter M. A. (ed.) et al., Computational science – ICCS 2003. International conference, Melbourne, Australia and St. Petersburg, Russia, June 2–4, 2003. Proceedings, Part IV. Berlin: Springer (ISBN 3-540-40197-0/pbk). Lecture Notes in Computer Science 2660, 346-354 (2003). MSC: 60H30 60G12 60H10 PDFBibTeX XMLCite \textit{D. Xiu} et al., Lect. Notes Comput. Sci. 2660, 346--354 (2003; Zbl 1188.60038) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em A new stochastic approach to transient heat conduction modeling with uncertainty. (English) Zbl 1038.80003 Int. J. Heat Mass Transfer 46, No. 24, 4681-4693 (2003). MSC: 80A20 37N20 60H15 65C30 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, Int. J. Heat Mass Transfer 46, No. 24, 4681--4693 (2003; Zbl 1038.80003) Full Text: DOI
Lucor, D.; Xiu, D.; Su, C.-H.; Karniadakis, G. E. Predictability and uncertainty in CFD. (English) Zbl 1032.76662 Int. J. Numer. Methods Fluids 43, No. 5, 483-505 (2003). MSC: 76M35 76D05 PDFBibTeX XMLCite \textit{D. Lucor} et al., Int. J. Numer. Methods Fluids 43, No. 5, 483--505 (2003; Zbl 1032.76662) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em Modeling uncertainty in flow simulations via generalized polynomial chaos. (English) Zbl 1047.76111 J. Comput. Phys. 187, No. 1, 137-167 (2003). MSC: 76M35 76D05 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, J. Comput. Phys. 187, No. 1, 137--167 (2003; Zbl 1047.76111) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. (English) Zbl 1016.65001 Comput. Methods Appl. Mech. Eng. 191, No. 43, 4927-4948 (2002). MSC: 65C30 35R60 35J05 65C05 60H15 65N30 65F10 60H35 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, Comput. Methods Appl. Mech. Eng. 191, No. 43, 4927--4948 (2002; Zbl 1016.65001) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em The Wiener–Askey polynomial chaos for stochastic differential equations. (English) Zbl 1014.65004 SIAM J. Sci. Comput. 24, No. 2, 619-644 (2002). MSC: 65C30 65C05 60H10 34F05 60H35 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, SIAM J. Sci. Comput. 24, No. 2, 619--644 (2002; Zbl 1014.65004) Full Text: DOI
Xu, Jin; Xiu, Dongbin; Karniadakis, George Em A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations. (English) Zbl 1028.76020 J. Sci. Comput. 17, No. 1-4, 585-597 (2002). Reviewer: Kai Schneider (Marseille) MSC: 76F65 76M22 76D05 PDFBibTeX XMLCite \textit{J. Xu} et al., J. Sci. Comput. 17, No. 1--4, 585--597 (2002; Zbl 1028.76020) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em A semi-Lagrangian high-order method for Navier-Stokes equations. (English) Zbl 1028.76026 J. Comput. Phys. 172, No. 2, 658-684 (2001). MSC: 76M10 76M22 76D05 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, J. Comput. Phys. 172, No. 2, 658--684 (2001; Zbl 1028.76026) Full Text: DOI