@Article{IJNAM-3-186,
author = {P. Danumjaya and A. K. Pani},
title = {Numerical Methods for the Extended Fisher-Kolmogorov (EFK) Equation},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2006},
volume = {3},
number = {2},
pages = {186--210},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/896.html}
}