We compare linear and nonlinear Galerkin methods in their efficiency to red
uce infinite dimensional systems, described by partial differential equatio
ns, to low dimensional systems of ordinary differential equations, both con
cerning the effort in their application and the accuracy of the resulting r
educed system.
Important questions like the choice of the form of the ansatz functions (mo
des), the choice of the number m of modes and, finally, the construction of
the reduced system are addressed. For the latter point, both the linear or
standard Galerkin method making use of the Karhunen Loeve (proper orthogon
al decomposition) ansatz functions and the nonlinear Galerkin method, using
approximate inertial manifold theory, are used. In addition, also the post
-processing Galerkin method is compared with the other approaches. (C) 2001
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