Determining finite volume elements for the 2D Navier-Stokes equations Academic Article uri icon

abstract

  • We consider the 2D Navier-Stokes equations on a square with periodic boundary conditions. Dividing the square into N equal subsquares, we show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behavior of the solution itself is completely determined, provided N is large enough. We also establish a rigorous upper bound for N needed to determine the solutions to the Navier-Stokes equation in terms of the physical parameters of the problem. 1992.

published proceedings

  • Physica D: Nonlinear Phenomena

author list (cited authors)

  • Jones, D. A., & Titi, E. S.

citation count

  • 65

complete list of authors

  • Jones, Don A||Titi, Edriss S

publication date

  • November 1992