A compatible and conservative spectral element method on unstructured grids |
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Authors: | Mark A Taylor Aimé Fournier |
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Institution: | 1. Sandia National Laboratories, Albuquerque, NM, USA;2. National Center for Atmospheric Research, Mesoscale and Microscale Meteorology Division, Boulder, CO, USA |
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Abstract: | We derive a formulation of the spectral element method which is compatible on very general unstructured three-dimensional grids. Here compatible means that the method retains discrete analogs of several key properties of the divergence, gradient and curl operators: the divergence and gradient are anti-adjoints (the negative transpose) of each other, the curl is self-adjoint and annihilates the gradient operator, and the divergence annihilates the curl. The adjoint relations hold globally, and at the element level with the inclusion of a natural discrete element boundary flux term. |
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Keywords: | Spectral element Finite element Mimetic Compatible Support operators Atmospheric modeling Shallow-water equations Sphere Conservation Local conservation Unstructured grids Cubed sphere |
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