On the Convergence of Stochastic Finite Elements
- Sandia National Laboratories
We investigate the rate of convergence of stochastic basis elements to the solution of a stochastic operator equation. As in deterministic finite elements, the solution may be approximately represented as the linear combination of basis elements. In the stochastic case, however, the solution belongs to a Hilbert space of functions defined on a cross product domain endowed with the product of a deterministic and probabilistic measure. We show that if the dimension of the stochastic space is n, and the desired accuracy is of order {var_epsilon}, the number of stochastic elements required to achieve this level of precision, in the Galerkin method, is on the order of | ln {var_epsilon} |{sup n}.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 791887
- Report Number(s):
- SAND2001-3142
- Country of Publication:
- United States
- Language:
- English
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