A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient

Abstract

Abstract In this paper, an efficient finite element scheme is presented for a class of fourth-order nonlinear parabolic problems with variable coefficient. To deal with second-order term in weak formulation, we choose the cubic B-spline function as a trial function. Rigorous error estimates are derived for both semi-discrete and fully-discrete schemes. We provide a numerical example to confirm our theoretical results.

Keywords

• Cubic B-spline
• Finite element method
• Nonlinear parabolic equation
• Variable coefficient
• Error estimate