A Comparative Study of Characteristic Finite Element and Characteristic Finite Volume Methods for Convection-Diffusion-Reaction Problems on Triangular Grids

Abstract

The paper aims to compare the accuracy and robustness of the characteristic finite element method (CFEM) and characteristic finite volume method (CFVM) for solving convection-diffusion-reaction problems on two-dimensional triangular grids. The tests are performed on a square unit domain, to which an advective field is imposed in a domain. The results show that the CFEM gives less accurate solution than CFVM for the rotation of a slotted-cylinder and rotation of Gaussian cone problems. Moreover, CFEM gives oscillate solution while the CFVM provides an oscillation-free solution for the skew flow to the grid problem.