Bubble finite elements for the primitive equations of the ocean |
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Authors: | F Guillén-González D Rodríguez-Gómez |
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Institution: | (1) Department EDAN, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain;(2) Exobiology Branch, MS 239-4, NASA Ames Research Center, Moffett Field, California, 94035, USA |
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Abstract: | We introduce in this paper two original Mixed methods for the numerical resolution of the (stationary) Primitive Equations
(PE) of the Ocean. The PE govern the behavior of oceanic flows in shallow domains for large time scales. We use a reduced
formulation (Lions et al. 28]) involving horizontal velocities and surface pressures. By using bubble functions constructed
ad-hoc, we are able to define two stable Mixed Methods requiring a low number of degrees of freedom. The first one is based on the
addition of bubbles of reduced support to velocities elementwise. The second one makes use of conic bubbles of extended support along the vertical coordinate. The latter constitutes a genuine mini-element for the PE, e.g., it requires the least number of extra degrees of freedom to stabilize piecewise linear hydrostatic pressures.
Both methods verify a specific inf-sup condition and provide stability and convergence. Finally, we compare several numerical
features of the proposed pairs in the context of other FE methods found in the literature. |
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Keywords: | 65N30 76M10 86A05 |
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