TY - JOUR
T1 - Determining finite volume elements for the 2D Navier-Stokes equations
AU - Jones, Don A.
AU - Titi, Edriss S.
N1 - Funding Information:
Part of the work was done while the authors enjoyedth eh ospitalitoyf the Centefro r Nonlinear Studiesa ndthe Instituteo f Geophysicasn d PlanetarPyh ysicsa tLos AlamosN ationaLl abo-ratoryT. he work of E.S.T. was partlys upported by AFOSR, NSF Grant DMS-8915672a, ndthe US Army ResearcOh fficet hroughth eM SI, Cot-nell University.
PY - 1992/11/1
Y1 - 1992/11/1
N2 - 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.
AB - 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.
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U2 - 10.1016/0167-2789(92)90233-D
DO - 10.1016/0167-2789(92)90233-D
M3 - Article
AN - SCOPUS:0039085599
SN - 0167-2789
VL - 60
SP - 165
EP - 174
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -