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Numerical methods for the extended Fisher-Kolmogorov (EFK) equation

DSpace at IIT Bombay

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Title Numerical methods for the extended Fisher-Kolmogorov (EFK) equation
 
Creator DANUMJAYA, P
PANI, AK
 
Subject velocity selection
marginal stability
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
 
Description 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.
 
Publisher ISCI-INSTITUTE SCIENTIFIC COMPUTING & INFORMATION
 
Date 2011-08-04T07:06:46Z
2011-12-26T12:54:36Z
2011-12-27T05:42:42Z
2011-08-04T07:06:46Z
2011-12-26T12:54:36Z
2011-12-27T05:42:42Z
2006
 
Type Article
 
Identifier INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 3(2), 186-210
1705-5105
http://dspace.library.iitb.ac.in/xmlui/handle/10054/9279
http://hdl.handle.net/10054/9279
 
Language en