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A cubic B-spline finite element method for a class of fourth order nonlinear differential equation with variable coefficient
  • Dandan Qin,
  • Wenzhu Huang
Dandan Qin
Aviation University of the Air Force

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Wenzhu Huang
Guizhou Medical University
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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.