The alternating group explicit (AGE) iterative method for solving a Ladyzhenskaya model for stationary incompressible viscous flow

References

• Ladyzhenskaya , O. 1969 . The Mathematical Theory of Viscous Incompressible Flow , New York : Gordon and Breach .
   Google Scholar
• Ladyzhenskaya , O. 1970 . “ Modification of the Navier–Stokes equations for large velocity grdients ” . In Boundary Value Problems of Mathematical Physics and Related Aspects of Function Theory II , 57 – 69 . New York : Consultants Bureau . In:
   Google Scholar
• Ladyzhenskaya , O. 1970 . “ New equation for the description of the viscous incompressible fluids and solvability in the large of the boundary value problems for them ” . In Boundary Value Problems of Mathematical Physics V , 95 – 118 . Providence, RI : American Mathematical Society . In:
   Google Scholar
• Du , Q. and Gunzburger , M. D. 1990 . Finite-element approximations of a Ladyzhenskaya model for stationary incompressible viscous flow . SIAM Journal on Numerical Analysis , 27 : 1 – 19 .
   Google Scholar
• Du , Q. and Gunzburger , M. D. 1991 . Analysis of a Ladyzhenskaya model for incompressible viscous flow . Journal of Mathematical Analysis and Applications , 155 : 21 – 45 .
   Web of Science ®Google Scholar
• Smagorinsky , J. 1963 . General circulation experiments with the primitive equations, Part I: The basic experiment . Monthly Weather Review , 91 : 99 – 164 .
   Google Scholar
• Evans , D. J. and Sahimi , M. S. 1988 . The alternating group explicit (AGE) iterative method for solving parabolic equations. I: Two-dimensional problems . International Journal of Computer Mathematics , 24 : 311 – 341 .
   Web of Science ®Google Scholar
• Evans , D. J. and Sahimi , M. S. 1989 . The alternating group explicit (AGE) iterative method to solve parabolic and hyperbolic partial differential equations . Annual Review of Numerical Fluid Mechanics and Heat Transfer , 2 : 283 – 389 .
   Google Scholar
• Evans , D. J. and Sahimi , M. S. 1990 . The solution of nonlinear parabolic partial differential equations by the alternating group explicit (AGE) method . Computer Methods in Applied Mechanics and Engineering , 84 : 15 – 42 .
   Web of Science ®Google Scholar
• Evans , D. J. and Sahimi , M. S. 1992 . “ The AGE Solution of the biharmonic equation for the deflection of a uniformly loaded square plate ” . UK : Department of Computer Studies, Loughborough University . Report 748
   Google Scholar
• Sahimi , M. S. and Evans , D. J. 1994 . The numerical solution of a coupled system of elliptic equations using the AGE fractional scheme . International Journal of Computer Mathematics , 50 : 65 – 87 .
   Web of Science ®Google Scholar
• Du , Q. , Gunzburger , M. D. and Hou , L. S. 1995 . Analysis and finite element approximation of optimal control problems for a Ladyzhenskaya model for stationary, incompressible, viscous flows . Journal of Computational and Applied Mathematics , 61 : 323 – 343 .
   Google Scholar
• Gunzburger , M. 1989 . Finite Element Method for Viscous Incompressible Flow: A Guide to Theory Practice and Algorithms , Boston : Academic Press .
   Google Scholar
• Layton , W. 1996 . A nonlinear subgridscale model for incompressible viscous flow problems . SIAM Journal on Scientific Computing , 17 : 347 – 357 .
   Google Scholar
• Fairag , F. 2006 . Analysis and finite element approximation of a Ladyzhenskaya model for viscous flow in streamfunction form . Journal of Computational and Applied Mathematics , 206 : 374 – 391 .
   Google Scholar
• Fairag , F. 2005 . Finite element computations for viscous incompressible flows using pure-streamfunction equation of the Ladyzhenskaya equations . WSEAS Transactions on Mathematics , 4 : 493 – 499 .
   Google Scholar
• Fairag , F. 2003 . Numerical computations of viscous, incompressible flow problems using a two-level finite element method . SIAM Journal on Scientific Computing , 24 : 1919 – 1929 .
   Google Scholar
• Schieweck , F. On the order of two noncomforming finite element approximations of upwind type for the Navier-Stokes equations . Proceeding of the international Workshop on Numerical Methods for the Navier–Stokes Equations . October , Heidelberg. pp. 25 – 28 . Vieweg-Verlag . Notes on Numerical Fluid Mechanics
   Google Scholar