Title: Nonlinear Galerkin Method Using Chebyshev and Legendre  Polynomials
       I. The One Dimensional Case

Author: Jie Shen

Status: SIAM J. Numer. Anal. 32, 215--234, 1995

Abstract:

We present in this work a new strategy, stemming from the nonlinear
Galerkin method [.mt1.], for solving linear elliptic and nonlinear
dissipative evolution equations by using Chebyshev and Legendre
polynomials. The essential  idea is to decompose the solution into
a low mode part and a high mode part and to treat them separately.
The robustness of the method over the classical Galerkin method is
substantiated by rigorous error estimates and preliminary numerical
experiments.