@Article{IJNAM-3-186, author = {}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/896.html} }