A hybrid Hermite–discontinuous Galerkin method for hyperbolic systems with application to Maxwellʼs equations

A high order discretization strategy for solving hyperbolic initial–boundary value problems on hybrid structured–unstructured grids is proposed. The method leverages the capabilities of two distinct families of polynomial elements: discontinuous Galerkin discretizations which can be applied on elements of arbitrary shape, and Hermite discretizations which allow highly efficient implementations on staircased Cartesian grids. We demonstrate through numerical experiments in 1 + 1 and 2 + 1 dimensions that the hybridized method is stable and efficient.