Variations on Hermite Methods for Wave Propagation (Communications in Computational Physics, 2018)
Hermite methods, as introduced by Goodrich et al. in [15], combine Hermiteinterpolation and staggered (dual) grids to produce stable high order accurate schemesfor the solution of hyperbolic PDEs. We introduce three variations of this Hermitemethod which do not involve time evolution on dual grids. Computational evidenceis presented regarding stability, high order convergence, and dispersion/dissipationproperties for each new method. Hermite methods may also be coupled to discontinuousGalerkin (DG) methods for additional geometric flexibility [4]. An exampleillustrates the simplification of this coupling for Hermite methods.