High-order h-adaptive discontinuous Galerkin methods for ocean modelling
(2007) Ocean Dynamics : theoretical, computational oceanography and monitoring — Vol. 57, n° 2, p. 109-121 (2007)
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- 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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Citations
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 : theoretical, computational oceanography and monitoring, 57(2), 109-121. https://doi.org/10.1007/s10236-006-0093-y (Original work published 2007)