Long-time error estimation for semi-linear parabolic equations

Authors:
Tong Sun;Daria Filippova
Affiliations:
Department of Mathematics Statistics, Bowling Green University, Bowling Green, OH;Department of Mathematics Statistics, Bowling Green University, Bowling Green, OH
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 4
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Abstract

The long-time error estimation approach of Sun and Ewing (Dyn. Contin. Discrete Impuls. Systems Ser. B Appl. Algorithms, 9 (2002) 115-129) is applied here for the error analysis and estimation of linear and semilinear parabolic partial differential equations. The analysis is carried out using the stability-smoothing indicator, the smoothing assumption, the moving attractor, the exact error propagation and the two-level error propagation analysis introduced by Sun and Ewing (Dyn. Contin. Discrete Impuls. Systems Ser. B Appl. Algorithms, 9 (2002) 115-129). Moreover, an inverse elliptic projection is employed here as a key technique in dealing with the spatial discretization error. The error estimates obtained are uniform in time. The results are substantiated by a complete mathematical analysis and numerical experiments.