Numerical solution of the Primitive Equations of the ocean by the Orthogonal Sub-Scales VMS method

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• 作者：Tomá ; s Chacó ; n Rebollo^a ; ^chacon@us.es ; Macarena Gó ; mez Má ; rmol^b ; ^{macarena@us.es} ; Isabel Sá ; nchez Muñ ; oz^b ; ^{isanchez@us.es}
• 关键词：Primitive Equations of the ocean ; VMS methods ; OSS method ; Finite elements ; Stability ; convergence ; error estimates ; Numerical tests
• 刊名：Applied Numerical Mathematics
• 出版年：2012
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：April, 2012
• 卷：62
• 期：4
• 页码：342-359
• 文件大小：491 K

摘要

This paper deals with the development of efficient numerical solvers for the Primitive Equations of the ocean. We consider weak solutions of a reduced model that includes the horizontal velocity and the surface pressure. We derive the numerical approximation of this model by the Orthogonal Sub-Scales (OSS) method via finite elements discretization. We perform the numerical analysis of this discretization (stability, convergence, error estimates) for a linearized model, obtaining optimal error estimates for 2D flows. This analysis is based upon a specific inf-sup condition for the OSS discretization. We also perform some numerical tests for the non-linear Primitive Equations, that confirm the theoretical convergence order expectations, and show an improved convergence with respect to standard mixed methods.