Convergence of approximate attractors for a fully discrete system for reaction-diffusion equations
作者:
Jie Shen,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1989)
卷期:
Volume 10,
issue 11-12
页码: 1213-1234
ISSN:0163-0563
年代: 1989
DOI:10.1080/01630568908816354
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
The reaction-diffusion equations are approximated by a fully discrete system: a Legendre-Galerkin approximation for the space variables and a semi-implicit scheme for the time integration. The stability and the convergence of the fully discrete system are established. It is also shown that, under a restriction on the space dimension and the growth rate of the nonlinear term, the approximate attractors of the discrete finite dimensional dynamical systems converge to the attractor of the original infinite dimensional dynamical systems. An error estimate of optimal order is derived as well without any further regularity assumption.
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