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Article Dans Une Revue Ocean Dynamics Année : 2007

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

Résumé

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.
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Dates et versions

hal-01006928 , version 1 (22-01-2018)

Identifiants

Citer

Paul-Emile Bernard, Nicolas Chevaugeon, Vincent Legat, Éric Deleersnijder, Jean-François Remacle. High-order h-adaptive discontinuous Galerkin methods for ocean modelling. Ocean Dynamics, 2007, 57 (2), pp.109-121. ⟨10.1007/s10236-006-0093-y⟩. ⟨hal-01006928⟩
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