A. Pestiaux, S.A. Melchior, J.F. Remacle, T. Kärnä, T. Fichefet and J. Lambrechts Discontinuous Galerkin finite element discretization of a strongly anisotropic diffusion operator International Journal for Numerical Methods in Fluids 75
In this paper, the discretization of a diffusion equation with a strong anisotropy by a discontinuous Galerkin finite element method is investigated. Two penalty factors from the literature have been improved and established from the coercivity property, in order to ensure stability and especially the efficiency of the system. The oriented penalty factor guarantees the weakest spurious numerical diffusion (right figure) and allows to have a well-conditioned system. Finally, this factor is used in a physical application : an idealized Arctic Ocean.
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