Abstract
In this paper we investigate mathematically and numerically the two-dimensional stochastic steady-state incompressible Navier---Stokes equations with an additive random noise represented by a series in terms of truncated standard normal random variables and orthogonal basis functions. The existence and uniqueness of solutions are established. A statistical error estimate for the finite element methods is derived. A computational approach involving eigen-bases for a stochastic elliptic system is discussed and results of numerical tests are presented to validate the method.
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