## Upper semicontinuity of attractors for linear multistep methods approximating sectorial evolution equations

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- by Adrian T. Hill and Endre Süli PDF
- Math. Comp.
**64**(1995), 1097-1122 Request permission

## Abstract:

This paper sets out a theoretical framework for approximating the attractor $\mathcal {A}$ of a semigroup $S(t)$ defined on a Banach space*X*by a

*q*-step semidiscretization in time with constant steplength

*k*. Using the one-step theory of Hale, Lin and Raugel, sufficient conditions are established for the existence of a family of attractors $\{ {\mathcal {A}_k}\} \subset {X^q}$, for the discrete semigroups $S_k^n$ defined by the numerical method. The convergence properties of this family are also considered. Full details of the theory are exemplified in the context of strictly $A(\alpha )$-stable linear multistep approximations of an abstract dissipative sectorial evolution equation.

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## Additional Information

- © Copyright 1995 American Mathematical Society
- Journal: Math. Comp.
**64**(1995), 1097-1122 - MSC: Primary 65J05; Secondary 34G20, 47H20, 47N20, 58F13, 65L06, 65M12
- DOI: https://doi.org/10.1090/S0025-5718-1995-1297470-2
- MathSciNet review: 1297470