Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions

Cai, Wentao; Li, Buyang; Li, Ying

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S103-S147

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 $L^p$-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.

Classification : 65N30, 76M05
Keywords: Navier–Stokes, variable density, finite element, convergence, maximal $L^p$-regularity

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