| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S103 - S147 | |
| DOI | https://doi.org/10.1051/m2an/2020029 | |
| Published online | 26 February 2021 | |
Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions
1
Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P.R. China
2
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
3
School of Computer Engineering and Science, Shanghai University, Shanghai 2000444, P.R. China
* Corresponding author: buyang.li@polyu.edu.hk
Received:
18
November
2018
Accepted:
17
April
2020
An error estimate is presented for a fully discrete, linearized and stabilized finite element method for solving the coupled system of nonlinear hyperbolic and parabolic equations describing incompressible flow with variable density in a two-dimensional convex polygon. In particular, the error of the numerical solution is split into the temporal and spatial components, separately. The temporal error is estimated by applying discrete maximal Lp-regularity of time-dependent Stokes equations, and the spatial error is estimated by using energy techniques based on the uniform regularity of the solutions given by semi-discretization in time.
Mathematics Subject Classification: 65N30 / 76M05
Key words: Navier–Stokes / variable density / finite element / convergence / maximal Lp-regularity
© EDP Sciences, SMAI 2021
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