Volume 12, Issue 1
Second Order Decoupled Implicit/Explicit Method of the Primitive Equations of the Ocean I: Time Discretization

Int. J. Numer. Anal. Mod., 12 (2015), pp. 1-30.

Published online: 2015-12

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• Abstract

In this article, we propose the time discretization of the second order decoupled implicit/explicit method of the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side. We deduce the second order optimal error estimates on the $L^2$ and $H^1$ norms of the time discrete velocity and density and the $L^2$ norm of the time discrete pressure under the restriction of the time step $0<\tau\leq\beta$ for some positive constant $\beta$. Also, we deduce some stability results on the time discrete solution under the same restriction on the time step.

• Keywords

Primitive equations of the ocean, stability, optimal error estimate, second order decoupled implicit/explicit method.

65N30, 76M10

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@Article{IJNAM-12-1, author = {}, title = {Second Order Decoupled Implicit/Explicit Method of the Primitive Equations of the Ocean I: Time Discretization}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {1}, pages = {1--30}, abstract = {

In this article, we propose the time discretization of the second order decoupled implicit/explicit method of the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side. We deduce the second order optimal error estimates on the $L^2$ and $H^1$ norms of the time discrete velocity and density and the $L^2$ norm of the time discrete pressure under the restriction of the time step $0<\tau\leq\beta$ for some positive constant $\beta$. Also, we deduce some stability results on the time discrete solution under the same restriction on the time step.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/476.html} }
TY - JOUR T1 - Second Order Decoupled Implicit/Explicit Method of the Primitive Equations of the Ocean I: Time Discretization JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 30 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/476.html KW - Primitive equations of the ocean, stability, optimal error estimate, second order decoupled implicit/explicit method. AB -

In this article, we propose the time discretization of the second order decoupled implicit/explicit method of the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side. We deduce the second order optimal error estimates on the $L^2$ and $H^1$ norms of the time discrete velocity and density and the $L^2$ norm of the time discrete pressure under the restriction of the time step $0<\tau\leq\beta$ for some positive constant $\beta$. Also, we deduce some stability results on the time discrete solution under the same restriction on the time step.

Yinnian He. (1970). Second Order Decoupled Implicit/Explicit Method of the Primitive Equations of the Ocean I: Time Discretization. International Journal of Numerical Analysis and Modeling. 12 (1). 1-30. doi:
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