Quasi-nodal third-order Bernstein polynomials in a discontinuous Galerkin model for flooding and drying
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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.
KeywordsDiscontinuous Galerkin Bernstein polynomials Inundation High-order methods
The authors gratefully acknowledge support through the Cluster of Excellence ‘CliSAP’ (EXC177), University of Hamburg, funded through the German Science Foundation (DFG), as well as through ASTARTE—Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3). The second author also acknowledges support through Advanced Simulation of Coupled Earthquake and Tsunami Events (ASCETE) funded by the Volkswagen foundation. Furthermore, the authors would like to thank the anonymous reviewers for their kind consideration and comments that helped improve the manuscript.
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