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...

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Detalhes bibliográficos
Autores: Frutos, Javier de, García-Archilla, Bosco, Volker, John, Novo, Julia
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
Descrição
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