TY - JOUR
T1 - Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations
Y1 - 2015
A1 - Francesco Ballarin
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
AB - In this work, we present a stable proper orthogonal decompositionâ€“Galerkin approximation for parametrized steady incompressible Navierâ€“Stokes equations with low Reynolds number.
PB - Wiley
UR - http://urania.sissa.it/xmlui/handle/1963/34701
U1 - 34915
U2 - Mathematics
U4 - 1
U5 - MAT/08
ER -
TY - JOUR
T1 - Stochastic optimal robin boundary control problems of advection-dominated elliptic equations
JF - SIAM Journal on Numerical Analysis
Y1 - 2013
A1 - Peng Chen
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
AB - 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.
VL - 51
ER -
TY - JOUR
T1 - Simulation-based uncertainty quantification of human arterial network hemodynamics
JF - International Journal Numerical Methods Biomedical Engineering
Y1 - 2012
A1 - Peng Chen
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
KW - uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction
AB - 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.
PB - Wiley
U1 - 6467
U2 - Mathematics
U4 - 1
U5 - MAT/08 ANALISI NUMERICA
ER -