Bubble finite elements for the primitive equations of the ocean

被引:7
|
作者
Guillén-González, F
Rodríguez-Gómez, D
机构
[1] Univ Sevilla, Dept EDAN, E-41080 Seville, Spain
[2] NASA, Ames Res Ctr, Exobiol Branch, Moffett Field, CA 94035 USA
关键词
D O I
10.1007/s00211-005-0626-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 P-1(x) circle times P-1(z) 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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页码:689 / 728
页数:40
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