Authors: Hauck, Moritz
Aizinger, Vadym
Frank, Florian
Hajduk, Hennes
Rupp, Andreas
Title: Enriched Galerkin method for the shallow-water equations
Language (ISO): en
Abstract: This work presents an enriched Galerkin (EG) discretization for the two-dimensional shallow-water equations. The EG finite element spaces are obtained by extending the approximation spaces of the classical finite elements by discontinuous functions supported on elements. The simplest EG space is constructed by enriching the piecewise linear continuous Galerkin space with discontinuous, element-wise constant functions. Similarly to discontinuous Galerkin (DG) discretizations, the EG scheme is locally conservative, while, in multiple space dimensions, the EG space is significantly smaller than that of the DG method. This implies a lower number of degrees of freedom compared to the DG method. The EG discretization presented for the shallow-water equations is well-balanced, in the sense that it preserves lake-at-rest configurations. We evaluate the method’s robustness and accuracy using various analytical and realistic benchmarks and compare the results to those obtained using the DG method. Finally, we briefly discuss implementation aspects of the EG method within our MATLAB / GNU Octave framework FESTUNG.
Subject Headings: enriched Galerkin
ocean modeling
local conservation
discontinuous Galerkin
shallow-water equations
finite elements
Subject Headings (RSWK): Finite Elemente
Issue Date: 2020-04
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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