01509nas 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-elliptic