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

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.

76D05, 76M10, 60H15

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@Article{IJNAM-10-727, author = {}, 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 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 & X. Yang. (1970). 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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