RT Journal Article ID 207aeb651cd2b5fd A1 Audouze , Christophe A1 Nair, Prasanth B. T1 SOME A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC AND PARABOLIC LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS JF International Journal for Uncertainty Quantification JO IJUQ YR 2014 FD 2014-08-29 VO 4 IS 5 SP 423 OP 454 K1 stochastic partial differential equations K1 a priori error estimation K1 chaos expansions K1 finite element methods K1 time-stepping stability K1 functional approximation AB We study some theoretical aspects of Legendre polynomial chaos based finite element approximations of elliptic and parabolic linear stochastic partial differential equations (SPDEs) and provide a priori error estimates in tensor product Sobolev spaces that hold under appropriate regularity assumptions. Our analysis takes place in the setting of finite-dimensional noise, where the SPDE coefficients depend on a finite number of second-order random variables. We first derive a priori error estimates for finite element approximations of a class of linear elliptic SPDEs. Subsequently, we consider finite element approximations of parabolic SPDEs coupled with a Θ-weighted temporal discretization scheme. We establish conditions under which the time-stepping scheme is stable and derive a priori rates of convergence as a function of spatial, temporal, and stochastic discretization parameters. We later consider steady-state and time-dependent stochastic diffusion equations and illustrate how the general results provided here can be applied to specific SPDE models. Finally, we theoretically analyze primal and adjoint-based recovery of stochastic linear output functionals that depend on the solution of elliptic SPDEs and show that these schemes are superconvergent. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,2f7b99cc281f2702,207aeb651cd2b5fd.html