메뉴 건너뛰기




Volumn 209, Issue 2, 2005, Pages 617-642

An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

Author keywords

Discontinuities; Polynomial chaos; Uncertainty

Indexed keywords

DIFFERENTIAL EQUATIONS; POLYNOMIALS;

EID: 21444449245     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.03.023     Document Type: Article
Times cited : (535)

References (17)
  • 1
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • N. Wiener The homogeneous chaos Am. J. Math. 60 1938 897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 3
    • 0033329066 scopus 로고    scopus 로고
    • Propagation of uncertainty in complex physical systems using a stochastic finite elements approach
    • R.G. Ghanem J. Red-Horse Propagation of uncertainty in complex physical systems using a stochastic finite elements approach Physica D 133 1999 137-144
    • (1999) Physica D , vol.133 , pp. 137-144
    • Ghanem, R.G.1    Red-Horse, J.2
  • 4
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • D. Xiu G.E. Karniadakis The Wiener-Askey polynomial chaos for stochastic differential equations SIAM J. Sci. Comput. 24 2 2002 619-644
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 5
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • D. Xiu 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
  • 7
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainty propagation schemes
    • O.P.L. Maitre H.N. Njam R.G. Ghanem O.M. Knio Multi-resolution analysis of Wiener-type uncertainty propagation schemes J. Comput. Phys. 197 2004 502-531
    • (2004) J. Comput. Phys. , vol.197 , pp. 502-531
    • Maitre, O.P.L.1    Njam, H.N.2    Ghanem, R.G.3    Knio, O.M.4
  • 8
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using Galerkin finite element techniques
    • M.K. Deb I. Babuška J.T. Oden Solution of stochastic partial differential equations using Galerkin finite element techniques Comput. Methods Appl. Mech. Eng. 190 2001 6359-6372
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.190 , pp. 6359-6372
    • Deb, M.K.1    Babuška, I.2    Oden, J.T.3
  • 9
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • R.H. Cameron W.T. Martin The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals Ann. Math. 48 1947 385
    • (1947) Ann. Math. , vol.48 , pp. 385
    • Cameron, R.H.1    Martin, W.T.2
  • 12
    • 21444444175 scopus 로고    scopus 로고
    • Multi-element generalized polynomial chaos for differential equations with random imputs: Algorithms and applications
    • Ph.D. Thesis, Brown University (in preparation)
    • X. Wan, Multi-element generalized polynomial chaos for differential equations with random imputs: Algorithms and applications, Ph.D. Thesis, Brown University (in preparation)
    • Wan, X.1
  • 13
    • 0013201448 scopus 로고
    • Dynamical properties of truncated Wiener-Hermite expansions
    • S.A. Orszag L.R. Bissonnette Dynamical properties of truncated Wiener-Hermite expansions Phys. Fluids 10 12 1967 2603-2613
    • (1967) Phys. Fluids , vol.10 , Issue.12 , pp. 2603-2613
    • Orszag, S.A.1    Bissonnette, L.R.2
  • 15
    • 16244388194 scopus 로고    scopus 로고
    • Stochastic solutions for the two-dimensional advection-diffusion equation
    • X. Wan D. Xiu G.E. Karniadakis Stochastic solutions for the two-dimensional advection-diffusion equation SIAM J. Sci. Comput. 26 2 2004 578-590
    • (2004) SIAM J. Sci. Comput. , vol.26 , Issue.2 , pp. 578-590
    • Wan, X.1    Xiu, D.2    Karniadakis, G.E.3
  • 16
    • 0242370956 scopus 로고    scopus 로고
    • Sparse finite elements for elliptic problems with stochastic data
    • C. Schwab R.A. Todor Sparse finite elements for elliptic problems with stochastic data Numer. Math. 95 2003 707-734
    • (2003) Numer. Math. , vol.95 , pp. 707-734
    • Schwab, C.1    Todor, R.A.2
  • 17
    • 10444254180 scopus 로고    scopus 로고
    • Numerical analysis of Galerkin FEM for stochastic elliptic PDEs
    • Ph.D. Thesis, ETHZ (in preparation)
    • R.A. Todor, Numerical analysis of Galerkin FEM for stochastic elliptic PDEs, Ph.D. Thesis, ETHZ (in preparation)
    • Todor, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.