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

2007; Springer Science+Business Media; Volume: 57; Issue: 2 Linguagem: Inglês

10.1007/s10236-006-0093-y

1616-7341

Paul-Émile Bernard, Nicolas Chevaugeon, Vincent Legat, Éric Deleersnijder, Jean‐François Remacle,

Numerical methods for differential equations

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.