Marion, Martine; Temam, Roger Nonlinear Galerkin methods. (English) Zbl 0683.65083 SIAM J. Numer. Anal. 26, No. 5, 1139-1157 (1989). This paper contains: the nonlinear Galerkin method and states the convergence result for the method; the proof of convergence; the statement and proof of an improved convergence result; two examples, namely the Kuramoto-Sivashinsky equation and the two-dimensional Navier- Stokes equations, showing that the results apply to these equations. Reviewer: N.F.F.Ebecken Cited in 3 ReviewsCited in 156 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65J15 Numerical solutions to equations with nonlinear operators 35Q30 Navier-Stokes equations 34G20 Nonlinear differential equations in abstract spaces 47J25 Iterative procedures involving nonlinear operators Keywords:integration method; nonlinear projection; long-term integration; nonlinear Galerkin method; convergence; Kuramoto-Sivashinsky equation; Navier-Stokes equations PDFBibTeX XMLCite \textit{M. Marion} and \textit{R. Temam}, SIAM J. Numer. Anal. 26, No. 5, 1139--1157 (1989; Zbl 0683.65083) Full Text: DOI