An Upwind Finite Volume Element Method Based on Quadrilateral Meshes for Nonlinear Convection-Diffusion Problems

摘要

Considering an upwind finite volume element method based on convex quadrilateral meshes for computing nonlinear convection-diffusion problems, some techniques, Such as calculus of variations, commutating operator, and the theory of prior error estimates and techniques, are adopted. Discrete maximum principle and optimal-order error estimates in H-1 norm for fully discrete method are derived to determine the errors in the approximate solution. Thus, the well-known problem [(Li et al., Generalized difference methods for differential equations: numerical analysis of finite volume methods, Marcel Dekker, New York, 2000), p 365.] has been solved. Some numerical experiments show that the method is a very effective engineering computing method for avoiding numerical dispersion and nonphysical oscillations.