Douglas N. Arnold, Differential Complexes and Numerical Stability, ICM 2002, Vol. I, 137-157, scan, arXiv:math/0212391
Douglas N. Arnold, Richard S. Falk, Ragnar Winther, Finite element exterior calculus: from Hodge theory to numerical stability, Bull. Amer. Math. Soc. (N.S.) 47, 281-354, 2010, arxiv/0906.4325, MR2594630, doi
Douglas N. Arnold, Richard S. Falk, Ragnar Winther, Finite element exterior calculus, homological techniques, and applications, Acta Numer. 15, 1-155, 2006, MR2007j:58002, doi
D. N. Arnold, M. E. Rognes, Stability of Lagrange elements for the mixed Laplacian, Calcolo 46 (2009), no. 4, 245–260, doi, MR2563784
The following vision may be relevant in future development of homological methods and applications of higher geometry in numerical analysis for hydrodynamic systems:
Dennis Sullivan, Algebra, topology and algebraic topology of 3D ideal fluids, arxiv/1010.2721 (has some ideas on need of a version of higher geometry, hence of homological methods in particular, is at the very end of the article)
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