An upwind finite volume element method based on quadrilateral meshes for nonlinear convection‐diffusion problems

Abstract

AbstractConsidering 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 H1 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. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009