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@article{Natale:2017:imanum/drx033,
author = {Natale, A and Cotter, CJ},
doi = {imanum/drx033},
journal = {IMA Journal of Numerical Analysis},
pages = {1388--1419},
title = {A variational H (div) finite-element discretization approach for perfect incompressible fluids},
url = {http://dx.doi.org/10.1093/imanum/drx033},
volume = {38},
year = {2017}
}

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TY  - JOUR
AB  - We propose a finite-element discretization approach for the incompressible Euler equations which mimicstheir geometric structure and their variational derivation. In particular, we derive a finite-element methodthat arises from a nonholonomic variational principle and an appropriately defined Lagrangian, where finite-elementH(div)vector fields are identified with advection operators; this is the first successful extensionof the structure-preserving discretization ofPavlovet al.(2009) to the finite-element setting. The resultingalgorithm coincides with the energy-conserving scheme proposed byGuzm anet al.(2016). Through thevariational derivation, we discover that it also satisfies a discrete analogous of Kelvin’s circulation theorem.Further, we propose an upwind-stabilized version of the scheme that dissipates enstrophy while preservingenergy conservation and the discrete Kelvin’s theorem. We prove error estimates for this version of thescheme, and we study its behaviour through numerical tests.
AU  - Natale,A
AU  - Cotter,CJ
DO  - imanum/drx033
EP  - 1419
PY  - 2017///
SN  - 0272-4979
SP  - 1388
TI  - A variational H (div) finite-element discretization approach for perfect incompressible fluids
T2  - IMA Journal of Numerical Analysis
UR  - http://dx.doi.org/10.1093/imanum/drx033
UR  - http://hdl.handle.net/10044/1/50007
VL  - 38
ER  -

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