Article
Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
Author/s | Frutos, Javier de
García-Archilla, Bosco Volker, John Novo, Julia |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2019-10 |
Deposit Date | 2023-12-19 |
Published in |
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Abstract | 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 ... 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 |
Funding agencies | Ministerio de Economía. España Agencia Estatal de Investigación. España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Junta de Castilla y León |
Project ID. | MTM2013-42538-P
MTM2016-78995-P MTM2015-65608-P VA024P17 |
Citation | De Frutos, J., García-Archilla, B., Volker, J. y Novo, J. (2019). Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization. IMA Journal of Numerical Analysis, 39 (4), 1747-1786. https://doi.org/10.1093/imanum/dry044. |
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