Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Finite Elements in Analysis and Design
Iterative Solvers for the Stochastic Finite Element Method
SIAM Journal on Scientific Computing
Mathematics and Computers in Simulation
Wave scattering by randomly shaped objects
Applied Numerical Mathematics
Finite Elements in Analysis and Design
Hi-index | 0.01 |
Flow and transport in tubes with rough surfaces play an important role in a variety of applications. Often the topology of such surfaces cannot be accurately described in all of its relevant details due to either insufficient data or measurement errors or both. In such cases, this topological uncertainty can be efficiently handled by treating rough boundaries as random fields, so that an underlying physical phenomenon is described by deterministic or stochastic differential equations in random domains. To deal with this class of problems, we use a computational framework, which is based on stochastic mappings to transform the original deterministic/stochastic problem in a random domain into a stochastic problem in a deterministic domain. The latter problem has been studied more extensively and existing analytical/numerical techniques can be readily applied. In this paper, we employ both a generalized polynomial chaos and Monte Carlo simulations to solve the transformed stochastic problem. We use our approach to describe transport of a passive scalar in Stokes' flow and to quantify the corresponding predictive uncertainty.