A high-order adaptive discontinuous Galerkin method for shallow water equations is presented that remains well-balanced, mass-conserving, and positivity-preserving with irregular sub-grid bathymetry and wet-dry fronts.
Implicit-explicit Runge-Kutta schemes and applica- tions to hyperbolic systems with relaxation
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High-order adaptive discontinuous finite elements for the shallow water equations with sub-grid irregular bathymetry
A high-order adaptive discontinuous Galerkin method for shallow water equations is presented that remains well-balanced, mass-conserving, and positivity-preserving with irregular sub-grid bathymetry and wet-dry fronts.