Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR STOCHASTIC BURGERS EQUATION

  • Lee, Hyung-Chun (Department of Mathematics Ajou University) ;
  • Nam, Yun (Department of Mathematics Ajou University)
  • Received : 2015.11.08
  • Published : 2017.01.01
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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.

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References

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