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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.
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참고문헌 (25)
참고문헌 신청
A. J. Chorin / 2009 / Stochastic Tools in Mathematics and Science / Springer
A. Jentzen / 2009 / Overcoming the order barrier in the numerical approxi-mation of stochastic partial differential equations with additive space-time noise / Proc. R. Soc.
C. A. J. Fletcher / 1984 / Computational Garlerkin methods / Springer-Verlag
D. Blomker / 2013 / Garlerkin approximations for the stochastic Burgers equa-tion / SIAM J. Numer. Anal 51 (1) : 694 ~ 715
E. Allen / 1998 / Finite element and difference approximation of some linear stochastic partial differential equations / Stoch. Stoch. Rep 64 (1-2) : 117 ~ 142
A. Jentzen / 2009 / Overcoming the order barrier in the numerical approxi-mation of stochastic partial differential equations with additive space-time noise / Proc. R. Soc.
C. A. J. Fletcher / 1984 / Computational Garlerkin methods / Springer-Verlag
D. Blomker / 2013 / Garlerkin approximations for the stochastic Burgers equa-tion / SIAM J. Numer. Anal 51 (1) : 694 ~ 715
E. Allen / 1998 / Finite element and difference approximation of some linear stochastic partial differential equations / Stoch. Stoch. Rep 64 (1-2) : 117 ~ 142
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