Fully Discrete Approximations to the Time-Dependent Navier–Stokes Equations with a Projection Method in Time and Grad-Div Stabilization

This paper studies fully discrete approximations to the evolutionary Navier–Stokes equations by means of inf-sup stable H1-conforming mixed finite elements with a grad-div type stabilization and the Euler incremental projection method in time. We get error bounds where the constants do not depend on...

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Detalles Bibliográficos
Autores: Frutos, Javier de, García-Archilla, Bosco, Novo, Julia
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/152695
Acceso en línea:https://hdl.handle.net/11441/152695
https://doi.org/10.1007/s10915-019-00980-9
Access Level:acceso abierto
Palabra clave:Error constants independent of the viscosity
Grad-div stabilization
Incompressible Navier–Stokes equations
Inf-sup stable finite element methods
Projection methods
Descripción
Sumario:This paper studies fully discrete approximations to the evolutionary Navier–Stokes equations by means of inf-sup stable H1-conforming mixed finite elements with a grad-div type stabilization and the Euler incremental projection method in time. We get error bounds where the constants do not depend on negative powers of the viscosity. We get the optimal rate of convergence in time of the projection method. For the spatial error we get a bound O(hk) for the L2 error of the velocity, k being the degree of the polynomials in the velocity approximation. We prove numerically that this bound is sharp for this method.