Uncertainty Quantification for Linear Hyperbolic Equations with Stochastic Process or Random Field Coefficients
Analysis of PDEs
2017-06-19 v2
Abstract
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein--Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.
Cite
@article{arxiv.1402.2156,
title = {Uncertainty Quantification for Linear Hyperbolic Equations with Stochastic Process or Random Field Coefficients},
author = {Andrea Barth and Franz G. Fuchs},
journal= {arXiv preprint arXiv:1402.2156},
year = {2017}
}