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Computational efficiency and approximate inertial manifolds for a Bénard convection system. (English) Zbl 0803.65122

A computational comparison between classical Galerkin and approximate inertial manifold methods is performed for the case of two-dimensional natural convection in a saturated porous material. The computations, supported by physical arguments and an abstract result regarding regularity of solutions to the governing equation, show the limitations of the approximate inertial manifold technique in obtaining improvements over the classical Galerkin method.

MSC:

65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
35Q55 NLS equations (nonlinear Schrödinger equations)

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