A high‐order triangular discontinuous Galerkin oceanic shallow water model

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A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: One-dimensional case (2015, methodology): “To obtain formally second-order accuracy, we use piecewise linear functions, which are represented by nodal Lagrange basis functions [10, 13], the latter being also employed as test functions.”
High‐order semi‐implicit time‐integrators for a triangular discontinuous Galerkin oceanic shallow water model (2009, methodology): “Since we do not have an analytic solution to the nonlinear Stommel problem, we then use the linear problem to ensure that we are achieving L(2) errors of 1 × 10 which is the exact numerical solution for eighth order polynomials with nr = 4 (see [20]).”
A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations (2009, background): “…Notre Dame, IN 46556, United States d The University of Texas at Austin, Austin, TX 78712, United States a r t i c l e i n f o Article history: Received 31 July 2008 Received in revised form 26 December 2008 Accepted 8 January 2009 Available online 23 January 2009 Keywords: Shallow water…”