Abstract
We propose a Discontinuous Galerkin scheme for the numerical solution of the Anisotropic (in particular, Hydrostatic) Stokes equations in Oceanography. The key is the introduction of interior penalties into the usual Stokes bilinear forms and, moreover, in the anisotropy (with respect to the horizontal and vertical directions) of these forms. Using \(\mathbb{P}_{k}\) discontinuous finite elements for velocity and pressure, we obtain discrete inf-sup stability independently on the ratio ɛ between the horizontal and vertical domain scales. Numerical tests are provided.
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Acknowledgements
First author was partially financed by MINECO grants MTM2015-69875-P (Spain) with the participation of FEDER. Second and third ones are partially supported by the research group FQM-315 of Junta de Andalucía (Spain).
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Guillén-González, F., Redondo-Neble, M.V., Rodríguez-Galván, J.R. (2017). Stable Discontinuous Galerkin Approximations for the Hydrostatic Stokes Equations. In: Mateos, M., Alonso, P. (eds) Computational Mathematics, Numerical Analysis and Applications. SEMA SIMAI Springer Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-49631-3_8
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DOI: https://doi.org/10.1007/978-3-319-49631-3_8
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