An L2 finite element approximation for the incompressible Navier–Stokes equations

Eunjung Lee, Wonjoon Choi, Heonkyu Ha

Research output: Contribution to journalArticlepeer-review

Abstract

This paper utilizes the Picard method and Newton's method to linearize the stationary incompressible Navier–Stokes equations and then uses an LL* approach, which is a least-squares finite element method applied to the dual problem of the corresponding linear system. The LL* approach provides an L2-approximation to a given problem, which is not typically available with conventional finite element methods for nonlinear second-order partial differential equations. We first show that the proposed combination of linearization scheme and LL* approach provides an L2-approximation to the stationary incompressible Navier–Stokes equations. The validity of L2-approximation is proven through the analysis of the weak problem corresponding to the linearized Navier–Stokes equations. Then, the convergence is analyzed, and numerical results are presented.

Original languageEnglish
Pages (from-to)1389-1404
Number of pages16
JournalNumerical Methods for Partial Differential Equations
Volume36
Issue number6
DOIs
Publication statusPublished - 2020 Nov 1

Bibliographical note

Funding Information:
information National Research Foundation of Korea, NRF-2015R1D1A1A01056909; NRF-2018R1D1A1B07042973

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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