New characteristic difference method with adaptive mesh for one-dimensional unsteady convection-dominated diffusion equations

Abstract

This article presents a kind of characteristic difference method with adaptive mesh for one-dimensional convection-dominated diffusion equations. The method can adaptively adjust the computational mesh according to the gradient of the solutions. Furthermore, the method in this article has second order accuracy for convective term and first order accuracy for diffusive term, which completely fits with the property of strong convection and weak diffusion for convection-dominated diffusion equations. Compared with the uniform mesh method, the method in this article has higher computational efficiency for linear and nonlinear convection-dominated diffusion equations.

Keywords:

• One-dimensional unsteady convection-dominated diffusion equation
• Adaptive mesh method
• New characteristic difference scheme
• Maximum norm error estimate