کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
500500 | 863091 | 2006 | 15 صفحه PDF | دانلود رایگان |
In this paper we focus on the long-term behavior of generalized polynomial chaos (gPC) and multi-element generalized polynomial chaos (ME-gPC) for partial differential equations with stochastic coefficients. First, we consider the one-dimensional advection equation with a uniform random transport velocity and derive error estimates for gPC and ME-gPC discretizations. Subsequently, we extend these results to other random distributions and high-dimensional random inputs with numerical verification using the algebraic convergence rate of ME-gPC. Finally, we apply our results to noisy flow past a stationary circular cylinder. Simulation results demonstrate that ME-gPC is effective in improving the accuracy of gPC for a long-term integration whereas high-order gPC cannot capture the correct asymptotic behavior.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 195, Issues 41–43, 15 August 2006, Pages 5582–5596