A NONLINEAR GALERKIN METHOD FOR THE BURGERS EQUATION

  • Kang, Sung-Kwon (Department of Mathematics, College of Natural Sciences, Chosun University) ;
  • Kwon, Yong-Hoon (Department of Mathematics, Pohang University of Science and Technology)
  • Published : 1997.04.01

Abstract

A nonlinear Galerkin method for the Burgers equation is considered. Due to the lack of the divergence free condition, the nonlinear term is treated differently compared to that of the Navier-Stokes equations. Strong convergence results are proved for the nonlinear Galerkin method.

Keywords

References

  1. Adv. Appl. mech. v.1 A mathematical model illustrating the theory of turbulence J. M. Burgers
  2. J. Sci. Comput v.8 Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin methd T. Dubois;J. Jauberteau;R. Temam
  3. Burgers' equation: a model for all reasons, in Numberical Solution of Partial Differential Equations C. Fletcher;J. Noye(ed.)
  4. Appl. Num. Math. v.6 The nonlinear Galerkin method in computational fluid dynamics F. Jauberteau;C. Rosier;R. Temam
  5. SIAM J. Num. Anal. v.26 Nonlinear Galerkin methods M. Marion;R. Temam
  6. Semigroup of Linear Operators and Applications to Partial Differential Equations A. Pazy
  7. The one-dimensional case, SIAM J. Num. Anal. v.32 Nonlinear Galerkin method using Chebyshev and Legendre polynomials I. J. Shen;R. Temam
  8. Navier-Stokes Equations: Theory and Numerical Analysis R. Temam
  9. Partial Differential Equations J. Wloka