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|High-order h-adaptive discontinuous Galerkin methods for ocean modelling|
|Bernard, P.-E.; Chevaugeon, N.; Legat, V.; Deleersnijder, E.; Remacle, J.-F. (2007). High-order h-adaptive discontinuous Galerkin methods for ocean modelling. Ocean Dynamics 57(2): 109-121. dx.doi.org/10.1007/s10236-006-0093-y|
|In: Ocean Dynamics. Springer-Verlag: Berlin. ISSN 1616-7341, more|
Equations; Modelling; Marine
shallow water equations H-adaptivity; discontinuous Galerkin; a posteriori error estimation
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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 hp+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.