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.
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Responsible editor: Tal Ezer
An erratum to this article can be found at http://dx.doi.org/10.1007/s10236-007-0127-0
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Bernard, PE., Chevaugeon, N., Legat, V. et al. High-order h-adaptive discontinuous Galerkin methods for ocean modelling. Ocean Dynamics 57, 109–121 (2007). https://doi.org/10.1007/s10236-006-0093-y
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DOI: https://doi.org/10.1007/s10236-006-0093-y