Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

By Michael Dumbser, Cedric Enaux, Eleuterio F. Toro. Journal of Computational Physics, 2008

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A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “(13)”
FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems (2010, background): “For the case of stiff source terms, we refer the reader to [16] and [17].”
On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws (2011, methodology): “The reconstruction polynomials wh are now evolved locally inside each element using the local space-time discontinuous Galerkin approach introduced in [11] and extended to multiple space dimensions in [10, 16].”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “Local space-time predictor The representation polynomials uh(x, t ) are now evolved in time according to a local weak formulation of the governing PDE in space-time, see [36, 35, 51, 41, 46, 10].”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “For two more general and fully numerical alternatives to the semi-analytical Cauchy-Kovalewski procedure see [11] and [10], where local space-time finite element methods are used in order to compute the polynomial Qi(x, t).”