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Volume 10, Issue 3
The Finite Element Method of a Euler Scheme for Stochastic Navier-Stokes Equations Involving the Turbulent Component

Y. Duan & X. Yang

Int. J. Numer. Anal. Mod., 10 (2013), pp. 727-744.

Published online: 2013-10

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  • Abstract

In this paper we study the finite element approximation for stochastic Navier-Stokes equations including a turbulent part. The discretization for space is derived by finite element method, and we use the backward Euler scheme in time discretization. We apply the generalized $L_2$-projection operator to approximate the noise term. Under suitable assumptions, strong convergence error estimations with respect to the fully discrete scheme are well proved.

  • Keywords

stochastic Navier-Stokes equations, finite element method, discrete scheme, and error estimation.

  • AMS Subject Headings

76D05, 76M10, 60H15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-727, author = {Y. Duan and X. Yang}, title = {The Finite Element Method of a Euler Scheme for Stochastic Navier-Stokes Equations Involving the Turbulent Component}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {3}, pages = {727--744}, abstract = {

In this paper we study the finite element approximation for stochastic Navier-Stokes equations including a turbulent part. The discretization for space is derived by finite element method, and we use the backward Euler scheme in time discretization. We apply the generalized $L_2$-projection operator to approximate the noise term. Under suitable assumptions, strong convergence error estimations with respect to the fully discrete scheme are well proved.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/592.html} }
TY - JOUR T1 - The Finite Element Method of a Euler Scheme for Stochastic Navier-Stokes Equations Involving the Turbulent Component AU - Y. Duan & X. Yang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 727 EP - 744 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/592.html KW - stochastic Navier-Stokes equations, finite element method, discrete scheme, and error estimation. AB -

In this paper we study the finite element approximation for stochastic Navier-Stokes equations including a turbulent part. The discretization for space is derived by finite element method, and we use the backward Euler scheme in time discretization. We apply the generalized $L_2$-projection operator to approximate the noise term. Under suitable assumptions, strong convergence error estimations with respect to the fully discrete scheme are well proved.

Y. Duan and X. Yang. (2013). The Finite Element Method of a Euler Scheme for Stochastic Navier-Stokes Equations Involving the Turbulent Component. International Journal of Numerical Analysis and Modeling. 10 (3). 727-744. doi:
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