00689nas a2200145 4500008004100000245009900041210006900140260001000209520018600219100002400405700002000429700002200449700002100471856005100492 2015 en d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, Francesco1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3470101509nas a2200145 4500008004100000245009700041210006900138300001600207490000700223520095300230100001501183700002201198700002101220856012201241 2013 eng d00aStochastic optimal robin boundary control problems of advection-dominated elliptic equations0 aStochastic optimal robin boundary control problems of advectiond a2700–27220 v513 aIn 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.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/stochastic-optimal-robin-boundary-control-problems-advection-dominated-elliptic01580nas a2200145 4500008004100000245008700041210006900128260001000197520093400207653011301141100001501254700002201269700002101291856012201312 2012 en d00aSimulation-based uncertainty quantification of human arterial network hemodynamics0 aSimulationbased uncertainty quantification of human arterial net bWiley3 aThis 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.10auncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/simulation-based-uncertainty-quantification-human-arterial-network-hemodynamics