@article {ChenQuarteroniRozza2013,
title = {Stochastic optimal robin boundary control problems of advection-dominated elliptic equations},
journal = {SIAM Journal on Numerical Analysis},
volume = {51},
number = {5},
year = {2013},
pages = {2700{\textendash}2722},
abstract = {In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided.},
doi = {10.1137/120884158},
author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza}
}
@article {10671,
title = {Simulation-based uncertainty quantification of human arterial network hemodynamics},
journal = {International Journal Numerical Methods Biomedical Engineering},
number = {SISSA preprint;},
year = {2012},
publisher = {Wiley},
abstract = {This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.},
keywords = {uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction},
author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza}
}