The discontinuous Galerkin method with Lax-Wendroff type time discretizations

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A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “Fully discrete one-step ADER-DG scheme The fully discrete one-step ADER-DG scheme [39, 101, 80] is obtained after multiplication of the governing PDE (1) by a test function Φk ∈ Uh, which is identical with the spatial basis functions, and subsequent integration over the space-time control volume Ti ”
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “Instead of using the traditional method of lines (MOL) approach based on third order TVD Runge-Kutta time stepping [64,65,43] and also instead of using a local strong form of the governing PDE such as the CauchyKovalewski procedure used in the original MUSCL [77] and ENO [44] schemes as well as in A”
On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws (2011, methodology): “[24], in the ADER schemes of Titarev and Toro [40, 41] and in the ADER-DG & LW-DG approaches presented in [15, 33].”