RT Journal Article ID 2bb5e03d09701c8b A1 Audouze , Christophe A1 Nair, Prasanth B. T1 A PRIORI ERROR ANALYSIS OF STOCHASTIC GALERKIN PROJECTION SCHEMES FOR RANDOMLY PARAMETRIZED ORDINARY DIFFERENTIAL EQUATIONS JF International Journal for Uncertainty Quantification JO IJUQ YR 2016 FD 2016-11-07 VO 6 IS 4 SP 287 OP 312 K1 randomly parametrized ordinary differential equations K1 generalized polynomial chaos expansions K1 stochastic Galerkin projection schemes K1 a priori error estimates K1 temporal discretization error K1 stochastic structural dynamics AB Generalized polynomial chaos (gPC) based stochastic Galerkin methods are widely used to solve randomly parametrized ordinary differential equations (RODEs). These RODEs are parametrized in terms of a finite number of independent and identically distributed second-order random variables. In this paper, we derive a priori error estimates for stochastic Galerkin approximations of RODEs accounting for the temporal and stochastic discretization errors. Under appropriate stochastic regularity assumptions, convergence rates are provided for first-order linear RODE systems and first-order nonlinear scalar RODEs. We also consider the case of second-order linear RODE systems that are routinely encountered in stochastic structural dynamics applications. Finally, some insights into the long-time behavior of gPC schemes are provided for a model problem drawing on the present analysis. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,55c0c92f02169163,2bb5e03d09701c8b.html