A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Pittsburgh, PA (United States)
Stochastic collocation method has proved to be an efficient method and been widely applied to solve various partial differential equations with random input data, including Navier- Stokes equations. However, up to now, rigorous convergence analyses are limited to linear elliptic and parabolic equations; its performance for Navier-Stokes equations was demonstrated mostly by numerical experiments. In this paper, we provide an error analysis of stochastic collocation method for a semi-implicit Backward Euler discretization for NSE and prove the exponential decay of the interpolation error in the probability space. Our analysis indicates that due to the nonlinearity, as final time T increases and NSE solvers pile up, the accuracy may be reduced significantly. Subsequently, the theoretical results are illustrated by the numerical test of time dependent fluid flow around a bluff body.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1649669
- Report Number(s):
- ORNL/TM--2014/79
- Country of Publication:
- United States
- Language:
- English
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