The High Order Finite Element Method for Steady Convection-diffusion-reaction Problems

A wide class of mass transfer problems is governed by the combined effect of convection, diffusion and reaction (CDR) processes. The finite element method using the standard Bubnov Galerkin method based on linear elements is widely applied for diffusion-dominated problems where the method produces accurate results. However, at high P'eclet numbers of transport problems, where the convection process dominates, this scheme gives rise to numerical oscillations in the solution which do not coincide with the physical phenomena. As a remedy, the high order finite element method is applied for CDR problems in this paper. Two numerical examples are taken as test cases to illustrate the capability of the high order finite element method of suppressing residual oscillations. An error convergence study is also presented to show the different characteristics of the convergence of h-refinement and p-refinement.     «

A wide class of mass transfer problems is governed by the combined effect of convection, diffusion and reaction (CDR) processes. The finite element method using the standard Bubnov Galerkin method based on linear elements is widely applied for diffusion-dominated problems where the method produces accurate results. However, at high P'eclet numbers of transport problems, where the convection process dominates, this scheme gives rise to numerical oscillations in the solution which do not coincide...     »