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Nonlinear Galerkin methods. (English) Zbl 0683.65083
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

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 (do not use 65Hxx)
35Q30 Navier-Stokes equations
34G20 Nonlinear differential equations in abstract spaces
47J25 Iterative procedures involving nonlinear operators
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