Volume 55, 2021Regular 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
|Page(s)||S103 - S147|
|Published online||26 February 2021|
Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions
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: email@example.com
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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