Accurate Computations on Inertial Manifolds
نویسندگان
چکیده
منابع مشابه
Arbitrarily Accurate Approximate Inertial Manifolds of Fixed Dimension
By employing an embedding result due to Mañé, and its recent strengthening due to Foias & Olson it is shown that a global attractor with finite fractal (box counting) dimension d lies within an arbitrarily small neighbourhood of a smooth graph over the space spanned by the first [[2d+1]] Fourier-Galerkin modes. The proof is, however, non-constructive.
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This paper discusses two numerical schemes that can be used to approximate inertial manifolds whose existence is given by one of the standard methods of proof. The methods considered are fully numerical, in that they take into account the need to interpolate the approximations of the manifold between a set of discrete gridpoints. As all the discretisations are refined the approximations are sho...
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Finite-dimensional inertial manifolds attract solutions to a nonlinear parabolic diierential equation at an exponential rate. In this paper inertial manifolds for multistep discretizations of such equations are studied. We provide an existence result for inertial manifolds under multistep discretization and show that these inertial manifolds converge to the inertial manifold of the original equ...
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A class of nonlinear dissipative partial diierential equations that possess nite dimensional attractive invariant manifolds is considered. An existence and perturbation theory is developed which uniies the cases of unstable manifolds and inertial mani-folds into a single framework. It is shown that certain approximations of these equations , such as those arising from spectral or nite element m...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2001
ISSN: 1064-8275,1095-7197
DOI: 10.1137/s1064827599351738