document: In recent years, the Discontinuous Galerkin (DG) method has emerged as a more thorough alternative for locally solving conservation laws of the shallow water equations with higher accuracy [21–27]. The DG method further involves finite element weak formulation to–inherently from conservation principles–shape a piecewise-polynomial solution over each local discrete cell, via local basis functions. On this basis, the DG polynomial accuracy is spanned by a set of coefficients, describing accuracy information, which are all locally evolved in time from conservation principles at the discrete level, with an arbitrary order of accuracy. A DG-based shallow water model appeals in providing higher quality solutions on very coarse meshes than a traditional finite volume counterpart, but is comparatively expensive to run and imposes a more restrictive stability condition for the CFL number [28,29].
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