Publication: A personal discussion on conservation, and how to formulate it
A personal discussion on conservation, and how to formulate it
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Abgrall, R. (2023). A personal discussion on conservation, and how to formulate it. In E. Franck, J. Fuhrmann, V. Michel-Dansac, & L. Navoret (Eds.), Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems : FVCA10, Strasbourg, France, October 30, 2023–November 03, 2023, Invited Contributions (No. 432; Issue 432, pp. 3–19). Springer. https://doi.org/10.1007/978-3-031-40864-9_1
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Since the celebrated theorem of Lax and Wendroff, we know a necessary condition that any numerical scheme for hyperbolic problem should satisfy: it should be written in flux form. A variant can also be formulated for the entropy. Even though some schemes, as for example those using continuous finite element, do not formally cast into this framework, it is a very convenient one. In this paper, we revisit this, introduce a different notion of local conservation which contains the previous one in one space dimension, and explore its cons
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Abgrall, R. (2023). A personal discussion on conservation, and how to formulate it. In E. Franck, J. Fuhrmann, V. Michel-Dansac, & L. Navoret (Eds.), Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems : FVCA10, Strasbourg, France, October 30, 2023–November 03, 2023, Invited Contributions (No. 432; Issue 432, pp. 3–19). Springer. https://doi.org/10.1007/978-3-031-40864-9_1