Quasi-nodal third-order Bernstein polynomials in a discontinuous Galerkin model for flooding and drying

A quasi-nodal discontinuous Galerkin (DG) model employs monotonicity preserving Bernstein polynomials as basis functions in combination with an efficient vertex-based slope limiter. As opposed to classical nodal Lagrange DG models, it simulates flooding and drying stably even with higher than second-order basis functions. We study the viability of the latter for inundation simulations in general and discuss the quality of the new basis functions. A subsequent numerical study demonstrates the conservation properties and local convergence rates of the new method.