Title: Long time stability and convergence for fully discrete
       nonlinear Galerkin method

Author: Jie Shen

Status: Appl. Anal. 38, 201-229, 1990

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 the
$L^\infty(\R^+,H^\alpha)\;(\alpha=0,1)$ stabilities of the fully
discrete nonlinear Galerkin methods under a less restrictive time step
constraint than that of the classical Galerkin methods.