UAM_Biblioteca

View Item 

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

Author
de Frutos, Javier; García-Archilla, Bosco; Novo Martín, Juliauntranslated
Entity
UAM. Departamento de Matemáticas
Publisher
Springer Nature
Date
2019-05-28
Citation
Journal of Scientific Computing 80.2 (2019): 1330-13688
ISSN
0885-7474
DOI
10.1007/s10915-019-00980-9
Funded by
Instituto de Investigación en Matemáticas (IMUVA), Universidad de Valladolid, Spain. Research supported under grants MTM2016-78995-P (AEI/MINECO, ES) and VA024P17, VA105G18 (Junta de Castilla y León, ES) cofinanced by FEDER funds (frutos@mac.uva.es) Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain. Research supported by Spanish MINECO under grant MTM2015-65608-P (bosco@esi.us.es) Departamento de Matemáticas, Universidad Autónoma de Madrid. Spain Research supported under grants MTM2016-78995-P (AEI/MINECO, ES) and VA024P17 (Junta de Castilla y León, ES) co financed by FEDER funds (julia.novo@uam.es)
Project
Gobierno de España. MTM2016-78995-P; Gobierno de España. MTM2015-65608-P; Gobierno de España. MTM2016-78995-P
Editor's Version
https://doi.org/10.1007/s10915-019-00980-9
Subjects
Error constants independent of the viscosity; Grad-div stabilization; Incompressible Navier–Stokes equations; Inf-sup stable finite element methods; Projection methods; Matemáticas
URI
http://hdl.handle.net/10486/689939
Note
This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-019-00980-9
Rights
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Abstract

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
Show full item record

Files in this item

Thumbnail
Size
1.065Mb
Format
PDF

Google™ Scholar:de Frutos, Javier - García-Archilla, Bosco - Novo Martín, Julia

This item appears in the following Collection(s)