An Improved Arrow–Hurwicz Method for the Steady-State Navier–Stokes Equations

Takhirov, Aziz
Çıbık, Aytekin Bayram
Eroğlu, Fatma Güler
Kaya Merdan, Songül
This paper presents a novel Arrow–Hurwicz type method for approximating the steady-state Navier Stokes equations using the finite element method. The novel method is inspired from artificial compressibility regularization of unsteady incompressible flows and allows one to circumvent solving saddle-point equations. We derive uniform boundedness and convergence to the exact solution whenever the small data condition for uniqueness of the solution is satisfied. A two-grid version of the scheme is also discussed. Numerical schemes show that the novel scheme significantly accelerates the convergence, without any additional computational cost or decreased accuracy.
Citation Formats
A. Takhirov, A. B. Çıbık, F. G. Eroğlu, and S. Kaya Merdan, “An Improved Arrow–Hurwicz Method for the Steady-State Navier–Stokes Equations,” JOURNAL OF SCIENTIFIC COMPUTING, vol. 96, pp. 1–21, 2023, Accessed: 00, 2023. [Online]. Available: