A new family of mixed finite elements in IR3
Numerische Mathematik
Optimal finite-element interpolation on curved domains
SIAM Journal on Numerical Analysis
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering
A stabilized space-time discretization for the primitive equations in oceanography
Numerische Mathematik
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
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In this work we introduce and analyze a numerical approximation of the primitive equations of the ocean by means of stabilized finite elements. We use a reduced formulation of these equations which only includes the (3D) horizontal velocity and the (2D) surface pressure. This, combined with the use of stabilized finite elements, provides a large reduction of degrees of freedom in comparison with previous mixed methods. The use of isoparametric prismatic finite elements provides good geometric adaptability to the topography. We perform an analysis of stability and convergence using the concept of static condensation on bubble spaces. Finally, we test our stabilized approximations in flows with complex 3D structure, including a real-life application. Specifically, we simulate the wind-driven circulation in Lake Neucha@?tel.