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.
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Acknowledgements
The author thanks the anonymous reviewers for their remarks and suggestions, as well as Claire Chainais-Hillairet, Maxime Herda and Simon Lemaire for fruitful discussions about this work. The author acknowledges support by the Labex CEMPI (ANR-11-LABX-0007-01).
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Moatti, J. (2023). A Skeletal High-Order Structure Preserving Scheme for Advection-Diffusion Equations. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 432. Springer, Cham. https://doi.org/10.1007/978-3-031-40864-9_29
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DOI: https://doi.org/10.1007/978-3-031-40864-9_29
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