Application of C-Bézier and H-Bézier basis functions to numerical solution of convection-diffusion equations

Abstract

Abstract Convection-diffusion equation is widely used to describe many engineering and physical problems. The finite element method is one of the most common tools for computing numerical solution. In 2003, Wang et al. proposed C-Bézier and H-Bézier basis functions which are not only a generalization of classical Bernstein basis functions but also have a free shape parameter bringing a lot of flexibility to geometrical modeling. In this paper, we adopt C-Bézier and H-Bézier basis functions to construct test and trial function spaces of finite element method to get numerical solution of convection-diffusion equations. Compared with Lagrange basis functions, numerical accuracy is improved by 1 − 3 $1-3$ order-of magnitudes which implies a much better approximation in simulating convection-diffusion problems. Several examples are presented to verify the feasibility and effectiveness of our method.

Keywords

• Convection-diffusion equation
• Finite element method
• C-Bézier basis function
• H-Bézier basis function