First-order decoupled method of the three-dimensional primitive equations of the ocean

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dc.contributor.authorChen, Zhangxing (John)
dc.contributor.authorHe, Y.
dc.contributor.authorZhang, Y.
dc.contributor.authorXu, H.
dc.date.accessioned2017-03-16T22:00:07Z
dc.date.available2017-03-16T22:00:07Z
dc.date.issued2016
dc.description.abstractThis paper is concerned with a first-order fully discrete decoupled method for solving the three-dimensional (3D) primitive equations of the ocean with the Dirichlet boundary conditions on the side, where a decoupled semi-implicit scheme is used for the time discretization, and the $P_1(P_1)-P_1-P_1(P_1)$ finite element for velocity, pressure, and density is used for the spatial discretization of these equations. The $H^1-L^2-H^1$ optimal error estimates for the numerical solution $(u_h^n,p_h^n,\theta_h^n)$ and the $L^2$ optimal error estimate for $(u^n_h,\theta_h^n)$ are established under the restriction of $0<h\le \beta_1$ and $0<\tau\le \beta_2$ for some positive constants $\beta_1$ and $\beta_2$. Moreover, numerical investigations are provided to show that the first-order decoupled method is of almost unconditional convergence with accuracy $\mathcal{O}(h+\tau)$ in the $H^1$-norm and $\mathcal{O}(h^2+\tau)$ in the $L^2$-norm for solving the 3D primitive equations of the ocean. Numerical results are given to verify the theoretical analysis.en_US
dc.description.grantingagencyNSERCen_US
dc.description.refereedYesen_US
dc.description.sponsorshipIndustrial consortium in Reservoir Simulation and Modelling; Foundation CMG; Alberta Innovates.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/30182
dc.identifier.grantnumberNSERC: IRCPJ365863-12; AITF: G203000197; AIEES: 3130.en_US
dc.identifier.urihttp://hdl.handle.net/1880/51866
dc.language.isoenen_US
dc.publisherSIAM Scientific Computingen_US
dc.publisher.departmentChemical & Petroleum Engineeringen_US
dc.publisher.facultySchulich School of Engineeringen_US
dc.publisher.institutionUniversity of Calgaryen_US
dc.relation.ispartofseries38;273-301
dc.titleFirst-order decoupled method of the three-dimensional primitive equations of the oceanen_US
dc.typejournal article
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