Ocean Dynamics

, Volume 57, Issue 2, pp 109–121 | Cite as

High-order h-adaptive discontinuous Galerkin methods for ocean modelling

  • Paul-Emile Bernard
  • Nicolas Chevaugeon
  • Vincent Legat
  • Eric Deleersnijder
  • Jean-François Remacle
Original paper

Abstract

In this paper, we present an h-adaptive discontinuous Galerkin formulation of the shallow water equations. For a discontinuous Galerkin scheme using polynomials up to order \( p \), the spatial error of discretization of the method can be shown to be of the order of \( h^{{p + 1}} \), where \(h\) is the mesh spacing. It can be shown by rigorous error analysis that the discontinuous Galerkin method discretization error can be related to the amplitude of the inter-element jumps. Therefore, we use the information contained in jumps to build error metrics and size field. Results are presented for ocean modelling problems. A first experiment shows that the theoretical convergence rate is reached with the discontinuous Galerkin high-order h-adaptive method applied to the Stommel wind-driven gyre. A second experiment shows the propagation of an anticyclonic eddy in the Gulf of Mexico.

Keywords

Shallow water equations H-adaptivity Discontinuous Galerkin A posteriori error estimation 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Paul-Emile Bernard
    • 1
  • Nicolas Chevaugeon
    • 3
  • Vincent Legat
    • 1
  • Eric Deleersnijder
    • 1
    • 2
  • Jean-François Remacle
    • 1
    • 3
  1. 1.Center for Systems Engineering and Applied Mechanics (CESAME)Université Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Institut d’Astronomie et de Géophysique G. LemaîtreUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Département d’Architecture, d’Urbanisme de Génie Civil et EnvironnementalUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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