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A skeletal high-order structure preserving scheme for advection-diffusion equations (2303.12062v2)
Published 21 Mar 2023 in math.NA and cs.NA
Abstract: We introduce a nonlinear structure preserving high-order scheme for anisotropic advection-diffusion equations. This scheme, based on Hybrid High-Order methods, can handle general meshes. It also has an entropy structure, and preserves the positivity of the solution. We present some numerical simulations showing that the scheme converges at the expected order, while preserving positivity and long-time behaviour.