A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data
Year: 2015
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 4 : pp. 549–581
Abstract
We analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size $H$ and solving a Stokes problem on a fine grid of size $h, h <<H$. This method gives optimal convergence for velocity in $H^1$-norm and for pressure in $L^2$-norm. The analysis mainly focuses on the loss of regularity of the solution at $t = 0$ of the Navier-Stokes equations.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2015.m1414
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 4 : pp. 549–581
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
-
A reduced-order two-grid method based on POD technique for the semilinear parabolic equation
Song, Junpeng | Rui, HongxingApplied Numerical Mathematics, Vol. 205 (2024), Iss. P.240
https://doi.org/10.1016/j.apnum.2024.07.012 [Citations: 0] -
Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations
Ray, Kallol | Goswami, Deepjyoti | Bajpai, SaumyaComputational Methods in Applied Mathematics, Vol. 24 (2024), Iss. 4 P.935
https://doi.org/10.1515/cmam-2023-0035 [Citations: 0] -
Two-Grid Mixed Finite-Element Approximations to the Navier–Stokes Equations Based on a Newton-Type Step
Durango, Francisco | Novo, JuliaJournal of Scientific Computing, Vol. 74 (2018), Iss. 1 P.456
https://doi.org/10.1007/s10915-017-0447-2 [Citations: 10] -
Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation
Shi, Dongyang | Yang, HuaijunApplied Mathematics and Computation, Vol. 310 (2017), Iss. P.40
https://doi.org/10.1016/j.amc.2017.04.010 [Citations: 12] -
Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data
Liang, Hongxia | Zhang, TongComputers & Mathematics with Applications, Vol. 77 (2019), Iss. 8 P.2221
https://doi.org/10.1016/j.camwa.2018.12.002 [Citations: 3] -
Two-Grid Finite Element Galerkin Approximation of Equations of Motion Arising in Oldroyd Fluids of Order One with Non-Smooth Initial Data
Goswami, D. | Damázio, P. D. | Yuan, J. Y. | Bir, B.Computational Mathematics and Mathematical Physics, Vol. 63 (2023), Iss. 4 P.659
https://doi.org/10.1134/S0965542523040061 [Citations: 0] -
Two-grid finite element method for the dual-permeability-Stokes fluid flow model
Nasu, Nasrin Jahan | Mahbub, Md. Abdullah Al | Hussain, Shahid | Zheng, HaibiaoNumerical Algorithms, Vol. 88 (2021), Iss. 4 P.1703
https://doi.org/10.1007/s11075-021-01091-z [Citations: 6] -
Generalized postprocessed approximations to the Navier–Stokes equations based on two grids
Durango, Francisco | Novo, JuliaJournal of Computational and Applied Mathematics, Vol. 368 (2020), Iss. P.112516
https://doi.org/10.1016/j.cam.2019.112516 [Citations: 2] -
On a three step two‐grid finite element method for the Oldroyd model of order one
Bir, Bikram | Goswami, DeepjyotiZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 101 (2021), Iss. 11
https://doi.org/10.1002/zamm.202000373 [Citations: 6] -
Optimal Error Estimates of the Penalty Finite Element Method for the Unsteady Navier–Stokes Equations with Nonsmooth Initial Data
Bir, Bikram | Goswami, Deepjyoti | Pani, Amiya K.Journal of Scientific Computing, Vol. 98 (2024), Iss. 2
https://doi.org/10.1007/s10915-023-02445-6 [Citations: 2]