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arXiv · 2607.00619

Hermite Semi-Lagrangian schemes on triangular meshes for advection equations

Ali Elarif·Michel Mehrenberger·Laurent Navoret
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Abstract

High-order Hermite semi-Lagrangian schemes on unstructured triangular grids are proposed for advection equations, based on Bell and Argyris finite elements. Nodal semi-Lagrangian schemes transport point values together with gradients and Hessians, while projection semi-Lagrangian schemes are basically semi-Lagrangian Discontinuous Galerkin schemes (SLDG) with straight remaining backward triangles and shared degrees of freedoms. Stability and convergence studies of the different schemes are carried out numerically.

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Ali Elarif, Michel Mehrenberger, Laurent Navoret. 2026-07-01. Hermite Semi-Lagrangian schemes on triangular meshes for advection equations. https://arxiv.org/abs/2607.00619

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