Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
This paper studies non inf-sup stable finite element approximations to the evolutionary Navier–Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby separately studying the effects of the different stabilization te...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/152698 |
| Acesso em linha: | https://hdl.handle.net/11441/152698 https://doi.org/10.1093/imanum/dry044 |
| Access Level: | acceso abierto |
| Palavra-chave: | Local projection stabilization Navier–Stokes equations Non inf-sup stable mixed finite elements |
| Resumo: | This paper studies non inf-sup stable finite element approximations to the evolutionary Navier–Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby separately studying the effects of the different stabilization terms. Error estimates are derived in which the constants are independent of inverse powers of the viscosity. For one of the methods, using velocity and pressure finite elements of degree l, it will be proved that the velocity error in L∞(0, T; L2(Ω)) decays with rate l + 1/2 in the case that ν ≤ h, with ν being the dimensionless viscosity and h being the mesh width. In the analysis of another method it was observed that the convective term can be bounded in an optimal way with the LPS stabilization of the pressure gradient. Numerical studies confirm the analytical results |
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