Geodesic
Rates of convergence of approximate attractors for parabolic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 67-111

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We estimate rates of convergence of global attractors of approximations to the global attractor of a semilinear parabolic equation. We consider a general equation for which all fixed points are hyperbolic and the Chafee–Infante equation having a nonhyperbolic fixed point. The results are applied to an implicit discretization of a parabolic equation. 
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     author = {V. S. Kolezhuk and S. Yu. Pilyugin},
     title = {Rates of convergence of approximate attractors for parabolic equations},
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V. S. Kolezhuk; S. Yu. Pilyugin. Rates of convergence of approximate attractors for parabolic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 67-111. http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a4/