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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.
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