Long time stability and convergence for fully discrete nonlinear galerkin methods

Abstract

The aim of this paper is to analyze the fully discrete nonlinear Galerkin methods, which are well suited to the long time integration of dissipative partial differential equations.

With the help of several time discrete Gronwall lemmas, we are able to prove L ^∞(IR⁺,H ^α ) (α=0,1) stabilities of the fully discrete nonlinear Galerkin methods under a less restrictive time step constraint than that of the classical Galerkin methods.

Keywords:

• Nonlinear Galerkin methods
• long time stability

AMS (MOS)::

• 35A40
• 35Q10
• 65J15

¹This work was supported in part by NSF grant DMS-8802596 and by Air Force Grant AFOSR-88103 and the Research Fund of Indiana University.

¹This work was supported in part by NSF grant DMS-8802596 and by Air Force Grant AFOSR-88103 and the Research Fund of Indiana University.

Notes

¹This work was supported in part by NSF grant DMS-8802596 and by Air Force Grant AFOSR-88103 and the Research Fund of Indiana University.