A structure-preserving split finite element discretization of the split wave equations

Werner Bauer and Jörn Behrens

Applied Mathematics and Computation, 2018, vol. 325, issue C, 375-400

Abstract: We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star operator. Our discretization framework conserves this geometrical structure and provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. We introduce lowest possible order discretizations of the split 1D wave equations, in which the discrete momentum and continuity equations follow by trivial projections onto piecewise constant FE spaces, omitting partial integrations. Approximating the Hodge-star by nontrivial Galerkin projections (GP), the two discrete metric equations follow by projections onto either the piecewise constant (GP0) or piecewise linear (GP1) space.

Keywords: Split linear wave equations; Split finite element method; Dispersion relation; Structure-preserving discretization; Shallow-water wave equations (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:325:y:2018:i:c:p:375-400

DOI: 10.1016/j.amc.2017.12.035

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