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

Wentao Cai, Buyang Li, Ying Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)S103-S147
Number of pages45
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume55
DOIs
Publication statusE-pub ahead of print - 26 Feb 2021

Keywords

  • Convergence
  • Finite element
  • Maximal Lp-regularity
  • Navier-Stokes
  • Variable density

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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