TY - JOUR
T1 - Numerical Methods for the Extended Fisher-Kolmogorov (EFK) Equation
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 186
EP - 210
PY - 2006
DA - 2006/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/896.html
KW - 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.
AB - <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>