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...
| Autores: | , , |
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| 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 |
| 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. |
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