High-order h-adaptive discontinuous Galerkin methods for ocean modelling
Résumé
In this paper, we present an h-adaptive Discontinuous Galerkin (DGM) formulation of the shallow water equations. For a DGM scheme using polynomials up to order p, the discretization error of the DGM can be shown to be of the order of h p+1. It can be shown by rigorous error analysis that the DGM 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. Some results are presented for ocean modeling problems. A first experiment shows that the theoretical convergence rate is reached with the DGM high-order h-adaptive method applied to the classical Stommel model. A second experiment shows the propagation of an anticyclonic eddy in the realistic domain of the Gulf of Mexico.
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