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http://dx.doi.org/10.4134/JKMS.j150673

SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR STOCHASTIC BURGERS EQUATION  

Lee, Hyung-Chun (Department of Mathematics Ajou University)
Nam, Yun (Department of Mathematics Ajou University)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 193-213 More about this Journal
Abstract
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 Karhunen-$Lo{\grave{e}}ve$ 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-$Lo{\grave{e}}ve$ expansion; sparse grids collocation; finite element method;
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