Spatial error estimates for a finite element viscosity-splitting scheme for the Navier-Stokes equations
In this paper, we obtain optimal first order error estimates for a fully discrete fractional-step scheme applied to the Navier-Stokes equations. This scheme uses decomposition of the viscosity in time and finite elements (FE) in space. In [15], optimal first order error estimates (for velocity and p...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::bfdc8ba0a086c55a8dee5c9bd539c7aa |
| Acceso en línea: | https://hdl.handle.net/11441/187141 |
| Access Level: | acceso abierto |
| Palabra clave: | Navier-Stokes Equations Splitting in time schemes Fully discrete schemes Error estimates Mixed formulation Stable finite elements |
| Sumario: | In this paper, we obtain optimal first order error estimates for a fully discrete fractional-step scheme applied to the Navier-Stokes equations. This scheme uses decomposition of the viscosity in time and finite elements (FE) in space. In [15], optimal first order error estimates (for velocity and pressure) for the corresponding time-discrete scheme were obtained, using in particular H2XH1 estimates for the approximations of the velocity and pressure. Now, we use this time-discrete scheme as an auxiliary problem to study a fully discrete finite element scheme, obtaining optimal first order approximation for velocity and pressure with respect to the max-norm in time and the H1XL2-norm in space. The proof of these error estimates are based on three main points: a) provide some new estimates for the time-discrete scheme (not proved in [15]) which must be now used, b) give a discrete version of the H2XH1 estimates in FE spaces, using stability in the W1,6XL6-norm of the FE Stokes projector, and c) the use of a weight function vanishing at initial time will let to hold the error estimates without imposing global compatibility for the exact solution. |
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