Year: 2006
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 186–210
Abstract
In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, some a priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and regularity results for the weak solutions are derived. Using $C^1$-conforming finite element method, optimal error estimates are established for the semidiscrete case. Finally, fully discrete schemes like backward Euler, two step backward difference and Crank-Nicolson methods are proposed, related optimal error estimates are derived and some computational experiments are discussed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-896
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 186–210
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: extended Fisher-Kolmogorov (EFK) equation Lyapunov functional weak solution existence uniqueness and regularity results finite element method semidiscrete method backward Euler two step backward difference and Crank-Nicolson schemes optimal estimates.