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There are very few results on mixed finite element methods on surfaces.
Manifolds, Tensor Analysis, and Applications
Abraham, R., Marsden, J. E., and Ratiu, T · 1988
Earlier work this paper cites.
Finite element exterior calculus, homological techniques, and applications
Arnold, D. N., Falk, R. S., and Winther, R · 2006
Earlier work this paper cites.
Numerical method for Darcy flow derived using Discrete Exterior Calculus
Hirani, A. N., Nakshatrala, K. B., and Chaudhry, J. H · 2008
Cited alongside, same era.
Finite element exterior calculus: from Hodge theory to numerical stability
Arnold, D. N., Falk, R. S., and Winther, R · 2010
Cited alongside, same era.
VanderZee, E., Hirani, A. N., Guoy, D., and Ramos, E. A · 2010
Later among the works it cites.
PyDEC: Algorithms and software for Discretization of Exterior Calculus, March 2011
Bell, N., and Hirani, A. N · 2011
Closest in time.
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