A stabilized space-time discretization for the primitive equations in oceanography

  • Authors:

  • T. Chacón Rebollo;D. Rodríguez Gómez

  • Affiliations:

  • Universidad de Sevilla, Departamento de Ecuaciones Diferenciales y Análisis Numérico, s/n. 41080, Sevilla, Avda. Reina Mercedes, Spain;Stanford University, Department of Mechanical Engineering, s/n. 41080, 262 Durand Building, 94305-4040, Stanford, CA, USA

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2004

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Abstract

In this work we introduce and analyze a space-time discretization for the Primitive Equations of the Ocean. We use a reduced formulation of these equations which only includes the (3D) horizontal velocity and the (2D) surface pressure (cf.[19,20]). We use a semi-implicit Backward Euler scheme for the time discretization. The spatial discretization in each time step is carried out through a Penalty Stabilized Method. This allows to circumvent the use of pairs of spaces satisfying the inf-sup condition, thus attempting a large saving of degrees of freedom. We prove stability estimates, from which we deduce weak convergence in two steps : first in space to a semi-discretisation in time, and then in time to the continuous problem. Finally, we show a numerical test in a real-life application. Specifically, we simulate the wind-driven circulation in the Leman lake.