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In this paper, we propose to apply the parametrized maximum-principle-preserving (MPP) flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to the discontinuous Galerkin (DG) method for solving the convection-diffusion equations. The feasibility of applying the proposed MPP flux limiters is based on the fact that cell averages of the DG solutions are updated in a conservative fashion (by using flux difference). Compared with the earlier approach in preserving the MPP property of DG solutions for convection-diffusion problems [Y. Zhang, X. Zhang, and C.-W. Shu, J. Comput. Phys., 234 (2012), pp. 295--316], we avoid the difficulty of rewriting cell averages as a convex combination of point values in the presence of diffusion terms for DG schemes of higher than second order accuracy. As a result, our proposed parametrized MPP flux limiter can be applied to DG methods of arbitrary high order. We theoretically prove that up to the third order accuracy can be preserved for...

High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations