Artículo
Analysis of the hydrostatic Stokes problem and finite-element approximation in unstructured meshes
Autor/es | Guillén González, Francisco Manuel
Rodríguez Galván, José Rafael |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2015-06 |
Fecha de depósito | 2017-02-06 |
Publicado en |
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Resumen | The stability of velocity and pressure mixed finite-element approximations in general meshes of the hydrostatic Stokes problem is studied, where two “inf-sup” conditions appear associated to the two constraints of the ... The stability of velocity and pressure mixed finite-element approximations in general meshes of the hydrostatic Stokes problem is studied, where two “inf-sup” conditions appear associated to the two constraints of the problem; namely incompressibility and hydrostatic pressure. Since these two constraints have different properties, it is not easy to choose finite element spaces satisfying both. From the analytical point of view, two main results are established; the stability of an anisotropic approximation of the velocity (using different spaces for horizontal and vertical velocities) with piecewise constant pressures, and the unstability of standard (isotropic) approximations which are stable for the Stokes problem, like the mini-element or the Taylor-Hood element. Moreover, we give some numerical simulations, which agree with the previous analytical results and allow us to conjecture the stability of some anisotropic approximations of the velocity with continuous piecewise linear pressure in unstructured meshes. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Identificador del proyecto | MTM2009-12927
MTM2012-32325 FQM-315 |
Cita | Guillén González, F.M. y Rodríguez Galván, J.R. (2015). Analysis of the hydrostatic Stokes problem and finite-element approximation in unstructured meshes. Numerische Mathematik, 130 (2), 225-256. |
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