Abstract:The discontinuous Galerkin finite element method (DGFEM) developed by Rhebergen et al. [1] offers a robust method for solving systems of nonconservative hyperbolic partial differential equations but, as we show here, does not satisfactorily deal with topography in shallow water flows at lowest order (so-called DG0, or equivalently finite volume). In particular, numerical solutions of the space-DG0 discretised one-dimensional shallow water equations over varying topography are not truly 'well-balanced'. A numer… Show more
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