Article
Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
Author/s | García-Archilla, Bosco
![]() ![]() ![]() ![]() ![]() ![]() ![]() Novo, Julia |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2023-09 |
Deposit Date | 2024-01-04 |
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Abstract | This paper studies fully discrete finite element approximations to the Navier–Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration, two implicit–explicit second-order backward ... This paper studies fully discrete finite element approximations to the Navier–Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration, two implicit–explicit second-order backward differentiation formulae (BDF2) schemes are applied. In both, the Laplacian is implicit while the nonlinear term is explicit, in the first one, and semiimplicit, in the second one. The grad-div stabilization allows us to prove error bounds in which the constants are independent of inverse powers of the viscosity. Error bounds of order in space are obtained for the error of the velocity using piecewise polynomials of degree to approximate the velocity together with second-order bounds in time, both for fixed time-step methods and for methods with variable time steps. A Courant Friedrichs Lewy (CFL)-type condition is needed for the method in which the nonlinear term is explicit relating time-step and spatial mesh-size parameters. |
Funding agencies | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Ministerio de Economía. España |
Project ID. | PGC2018-096265-B-I00
![]() PID2019-104141GB-I00 ![]() VA169P20 ![]() |
Citation | García-Archilla, B. y Novo, J. (2023). Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps. IMA Journal of Numerical Analysis, 43 (5), 2892-2933. https://doi.org/10.1093/imanum/drac058. |
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