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

Beisiegel, Nicole; Behrens, Jörn

doi:10.1007/s12665-015-4745-4

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

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Beisiegel, N., & Behrens, J. (2015). Quasi-nodal third-order Bernstein polynomials in a discontinuous Galerkin model for flooding and drying. Environmental Earth Sciences, 74(11), 7275-7284. doi:10.1007/s12665-015-4745-4.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0028-8EA0-5

Abstract

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.