An upwind finite-volume element scheme and its maximum-principle-preserving property for nonlinear convection-diffusion problem

作者：Gao Fuzheng^*; Yuan Yirang; Yang Danping

来源：International Journal for Numerical Methods in Fluids, 2008, 56(12): 2301-2320.

DOI：10.1002/fld.1623

• nonlinear
• convection-diffusion equation
• finite-volume element method
• maximum principle
• upwind method

For a class of nonlinear convection-diffusion equation in multiple space dimensions, a kind of upwind finite-volume element (UFVE) scheme is put forward. Some techniques, such as calculus of variations, commutating operators and prior estimates, are adopted. It is proved that the UFVE scheme is unconditionally stable and satisfies maximum principle. Optimal-order estimates in H-1-norm are derived to determine the error in the approximate solution. Numerical results are presented to observe the performance of the scheme.

• 出版日期2008-4-30
• 单位山东大学