Journal of the
Korean Mathematical Society JKMS

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the \linebreak Karhunen-Lo{\`{e}}ve expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.

Keywords: Burgers equation, Orstein-Uhlenbeck process, Karhunen-Lo{\`{e}}ve expansion, sparse grids collocation, finite element method

MSC numbers: 65M70, 76F65