In this talk, we will show that, to leading order, the correct approximative scheme is actually the post-processing Galerkin
method, and not the standard Galerkin
method as is commonly believed. The post-processing Galerkin scheme was introduced as an alternative to, and more efficient than, the nonlinear Galerkin method which is based on the theory of approximate inertial manifolds.
Inspired by this observation, we raise the question about the validity of the Galerkin type projection methods which are based on energy norms. In particular, the Galerkin method based on the Proper Orthogonal Decomposition (Karhunen Leove expansion). Similar questions can be asked in the context of data assimilation schemes.
Some computational evidence supporti
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