Hermite Semi-Lagrangian schemes on triangular meshes for advection equations
For computational scientists solving advection equations, this work extends high-order semi-Lagrangian methods to unstructured triangular meshes, but the results are incremental.
The paper proposes high-order Hermite semi-Lagrangian schemes on triangular meshes for advection equations, using Bell and Argyris finite elements. Numerical studies demonstrate stability and convergence.
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.