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Mimetic Spectral Elements #195

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Mimetic Spectral Elements #195

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@celdred celdred commented Jun 28, 2019

This pull request adds mimetic spectral elements (described at https://www.sciencedirect.com/science/article/pii/S0021999113006414 and https://arxiv.org/abs/1111.4304), both the primal and dual complexes. This is done by adding the relevant 1D H1 element for the dual complex: Extended Gauss Legendre (EGL); and the L2 edge elements associated with GLL and EGL. These are non-Ciarlet finite elements that use a basis that histopolates (http://people.math.sfu.ca/~nrobidou/public_html/prints/histogram/histogram.pdf) rather than interpolates. The nD deRham complex on hypercubes is then accessible using the variant keyword (either “mse” or “dualmse”) with the relevant elements (DQ, Q, RTCF, etc.).

It requires FEniCS/ufl#5 , FEniCS/fiat#29 and FInAT/FInAT#54

It also requires correct (integral-preserving) L2 pullbacks, which are implemented at #194.

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