Solution of the Navier Stokes Equation with a Colored Noise Forcing Term
We pose a version of the time-dependent incompressible Navier-Stokes equations with a stochastic forcing term. The finite element method is used to discretize the variational form of the problem. The stochastic forcing term is represented by a covariance function whose eigenvalues are employed in a truncated Karhunen-Loeve expansion. Finite element computations are applied to problems with both Gaussian and exponential covariance functions, and the appropriate rate of convergence is observed.