Super Upwinding Elements of Doubt and Discrete Differences of Opinion on the Numerical Muddling of the Incomprehensible Defective Confusion Equation

摘要

An extension of the Leonard third order consistent method for the convection diffusion equation, which is valid at infinite mesh Reynolds numbers and performs better than the Hughes scheme on standard test problems is proposed. In a Petrov-Galerkin scheme based on quadratic trial and cubic test functions, an interlaced sequence of three and five point difference expressions are found. When the optimum parameters are used, these formulas admit constant and exponential solution but give errors for linear expressions unless the Reclet number is zero.