Ju, Ning (2000) Numerical analysis of parabolic p-Laplacian: Approximation of trajectories. SIAM Journal on Numerical Analysis, 37 (6). pp. 1861-1884. ISSN 0036-1429. doi:10.1137/S0036142998332840. https://resolver.caltech.edu/CaltechAUTHORS:JUNsiamjna00
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Abstract
The long time numerical approximation of the parabolic p-Laplacian problem with a time-independent forcing term and sufficiently smooth initial data is studied. Convergence and stability results which are uniform for t is an element of [0, infinity) are established in the L-2, W-1,W-p norms for the backward Euler and the Crank-Nicholson schemes with the finite element method (FEM). This result extends the existing uniform convergence results for exponentially contractive semigroups generated by some semilinear systems to nonexponentially contractive semigroups generated by some quasilinear systems.
| Item Type: | Article | ||||||
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| Additional Information: | © 2000 Society for Industrial and Applied Mathematics. Received by the editors January 16, 1998; accepted for publication (in revised form) December 3, 1999; published electronically May 23, 2000. The author is deeply grateful to his adviser, Prof. Roger Temam, for precious advice, stimulating discussions, and helpful comments and owes much to his constant encouragement and support. The author sincerely thanks the referees for their careful reading of this article and for helpful comments which improve the manuscript. He also sincerely thanks Prof. Mitchell Luskin for his kind help and valuable suggestions. | ||||||
| Subject Keywords: | finite element methods, parabolic p-Laplacian, long-time dynamics, quasi-linear equations, uniform convergence, finite-element approximation, reaction-diffusion equations, differential-equations, systems, time, semicontinuity, attractors, stability, behavior, uniform | ||||||
| Issue or Number: | 6 | ||||||
| DOI: | 10.1137/S0036142998332840 | ||||||
| Record Number: | CaltechAUTHORS:JUNsiamjna00 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:JUNsiamjna00 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 857 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 31 Oct 2005 | ||||||
| Last Modified: | 08 Nov 2021 19:05 |
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