Stochastic galerkin discretization of the log-normal isotropic diffusion problem

Mathematical Models and Methods in Applied Sciences

Volumn 20, Issue 2, 2010, Pages 237-263

  Gittelson, C J ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Stochastic Galerkin methods; Stochastic partial differential equations

Indexed keywords

BEST APPROXIMATIONS; CONVERGENCE ANALYSIS; DIFFUSION COEFFICIENTS; EXACT SOLUTION; GALERKIN; GALERKIN DISCRETIZATION; GALERKIN PROJECTIONS; GAUSSIAN RANDOM VARIABLE; HERMITE; INFINITE SERIES; ISOTROPIC DIFFUSION; LOG-NORMAL; MODEL PROBLEMS; QUASI-OPTIMAL; RANDOM DIFFUSION; STANDARD FINITE ELEMENT; STOCHASTIC GALERKIN METHODS; STOCHASTIC PARTIAL DIFFERENTIAL EQUATION; WEAK FORMULATION;

ALGEBRA; COMPUTATIONAL FLUID DYNAMICS; DIFFUSION; PARTIAL DIFFERENTIAL EQUATIONS; RANDOM PROCESSES; RANDOM VARIABLES; STOCHASTIC SYSTEMS;

GALERKIN METHODS;

EID: 77951615802     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202510004210     Document Type: Article

References (17)

1. A. Andreev, M. Bieri and C. Schwab, Sparse tensor discretization of elliptic sPDEs, Tech. Rep. 2009-07, SAM, 2009, submitted.
2. I. Babuška, F. Nobile and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal. 45 (2007) 1005-1034 (electronic), doi: 10.1137/050645142.
3. 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 (electronic), doi: 10.1137/S0036142902418680. (Pubitemid 40645215)
4. M. Bieri, A sparse composite collocation finite element method for elliptic sPDEs, Tech. Rep. 2009-08, SAM, 2009, submitted.
5. M. Bieri and C. Schwab, Sparse high order FEM for elliptic sPDEs, Comput. Meth. Appl. Mech. Engrg. 198 (2009) 1149-1170, doi: 10.1016/j.cma.2008.08.019.
6. V. I. Bogachev, Gaussian Measures, Mathematical Surveys and Monographs, Vol. 62 (Amer. Math. Soc., 1998).
7. A. Cohen, R. DeVore and C. Schwab, Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs, Tech. Rep. 2009-02, SAM, 2009, In review.
8. G. Da Prato, An Introduction to Infinite-Dimensional Analysis (Springer-Verlag, 2006). [Revised and extended from the 2001 original by Da Prato].
9. M. K. Deb, I. M. Babuška and J. T. Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Comput. Meth. Appl. Mech. Engrg. 190 (2001) 6359-6372, doi: 10.1016/S0045-7825 (01) 00237-7. (Pubitemid 32984202)
10. R. A. DeVore, Nonlinear approximation, in Acta Numer., Vol. 4 (Cambridge Univ. Press, 1998), pp. 51-150.
11. P. Frauenfelder, C. Schwab and R. A. Todor, Finite elements for elliptic problems with stochastic coefficients, Comput. Meth. Appl. Mech. Engrg. 194 (2005) 205-228, doi: 10.1016/j.cma.2004.04.008. (Pubitemid 39637479)
12. H. G. Matthies and A. Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, Comput. Meth. Appl. Mech. Engrg. 194 (2005) 1295-1331, doi: 10.1016/j.cma.2004.05.027. (Pubitemid 40262932)
13. F. Nobile, R. Tempone and C. G. Webster, An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal. 46 (2008) 2411-2442, doi: 10.1137/070680540.
14. F. Nobile, R. Tempone and C. G. Webster, A sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal. 46 (2008) 2309-2345, doi: 10.1137/060663660.
15. W. Rudin, Real and Complex Analysis, 3rd edn. (McGraw-Hill, 1987).
16. R. A. Todor and C. Schwab, Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients, IMA J. Numer. Anal. 27 (2007) 232-261, doi: 10.1093/imanum/drl025.
17. K. Yosida, Functional Analysis, Grundlehren der Mathematischen Wissenschaften, Vol. 123 [Fundamental Principles of Mathematical Sciences] 6th edn. (Springer-Verlag, 1980).