Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos

Computer Methods in Applied Mechanics and Engineering

Volumn 191, Issue 43, 2002, Pages 4927-4948

  Xiu, Dongbin ^a   Em Karniadakis, George ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Polynomial chaos; Random diffusion; Uncertainty

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; CHAOS THEORY; COMPUTER SIMULATION; MONTE CARLO METHODS; PARTIAL DIFFERENTIAL EQUATIONS; POISSON DISTRIBUTION; POLYNOMIALS; STOCHASTIC CONTROL SYSTEMS; UNCERTAIN SYSTEMS;

RANDOM DIFFUSIVITY; STEADY STATE DIFFUSION PROBLEMS;

MECHANICAL ENGINEERING;

CHAOS; DIFFERENTIAL EQUATION; DIFFUSION; STATISTICAL ANALYSIS;

EID: 0037184252     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(02)00421-8     Document Type: Article

References (35)

1. Random field finite elements
2. Probabilistic finite elements for nonlinear structural dynamics
3. Applications of probabilistic finite element methods in elastic/plastic dynamics
4. The homogeneous chaos
5. Ingredients for a general purpose stochastic finite element formulation
6. Hermite expansion in Monte-Carlo simulations
7. Solution of stochastic partial differential equations using Galerkin finite element techniques
8. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
9. The Wiener-Askey polynomial chaos for stochastic differential equations
10. Some basic hypergeometric polynomials that generalize Jacobi polynomials
11. Modeling uncertainty in flow simulations via generalized polynomial chaos
12. Stochastic modeling of flow-structure iterations using generalized polynomial chaos
13. On randomized solutions of Laplace's equation
14. The random steady state diffusion problem. I. Random generalized solutions to Laplace's equation
15. The random steady state diffusion problem. II. Random solutions to nonlinear inhomogeneous, steady state diffusion problems
16. The random steady state diffusion problem. III. Solutions to random diffusion problems by the method of random successive approximations
17. Diffusion in random media
18. Stochastic partial differential equations: A modeling
19. Finite elements for stochastic media problems
20. Orthogonal functionals of the Poisson process
21. Three-dimensional stochastic finite element method for elasto-plastic bodies
22. On stationary processes in the plane