Academic Journal
Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
| العنوان: | Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps |
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| المؤلفون: | García-Archilla, Bosco, Novo, Julia |
| المساهمون: | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI), Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería, Ministerio de Ciencia, Innovación y Universidades (MICINN). España, Ministerio de Economía. España |
| بيانات النشر: | Oxford University Press / Institute of Mathematics and its Applications |
| سنة النشر: | 2024 |
| المجموعة: | idUS - Deposito de Investigación Universidad de Sevilla |
| مصطلحات موضوعية: | Incompressible Navier–Stokes equations, Variable step BDF2, Implicit–explicit methods, Graddiv stabilization, Robust error bounds |
| الوصف: | © The Author(s) 2022. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. ; 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. ; Ministerio de Ciencia, Innovación y Universidades PGC2018-096265-B-I00 - PID2019-104141GB-I00 ; Ministerio de Economía PID2019-104141GB-I00 - VA169P20 |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| ردمك: | 978-2-01-809626-8 2-01-809626-5 |
| Relation: | IMA Journal of Numerical Analysis, 43 (5), 2892-2933.; PGC2018-096265-B-I00; PID2019-104141GB-I00; VA169P20; https://academic.oup.com/imajna/article/43/5/2892/6748175; https://idus.us.es/handle//11441/152944 |
| الاتاحة: | https://idus.us.es/handle//11441/152944 |
| Rights: | Attribution-NonCommercial-NoDerivatives 4.0 Internacional ; http://creativecommons.org/licenses/by-nc-nd/4.0/ ; info:eu-repo/semantics/embargoAccess |
| رقم الانضمام: | edsbas.B57A9807 |
| قاعدة البيانات: | BASE |
| ردمك: | 9782018096268 2018096265 |
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