Abstract
This article presents an analogy existing between the concepts of approximate inertial manifolds in dynamical systems theory and multigrid methods in numerical analysis. In view of the large-time approximation of dissipative evolution equations in a turbulent regime, a new algorithm is proposed and studied that combines some ideas and concepts of inertial manifolds and multigrid methods. This article emphasizes theoretical questions. More practical (computational) questions will be investigated elsewhere.
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