A cubic B-spline finite element method for a class of fourth order
nonlinear differential equation with variable coefficient
Abstract
In this paper, the cubic B-spline element method is proposed for a class
of fourth order nonlinear parabolic problem with variable coefficient.
We prove the boundness of the approximate solutions of the semi-discrete
and fully discrete finite element schemes. The boundness is the basis of
error analysis of nonlinear parabolic problem, especially in the case of
fourth order term with variable coefficient. The error estimates are
discussed by constructing the energy functional in $L^2$ norm and
$H^2$ norm. Numerical results confirm our results of theoretical
analysis.