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I archive here the query box from homological algebra and finite element method.
Eric: The appearance of homological algebra in finite element methods goes back a lot earlier than Arnold. It is covered somewhat extensively in Robert Kotiuga’s (who happened to be John Baez’s dorm room mate at MIT) PhD dissertation:
- Kotiuga, P.R., Hodge Decompositions and Computational Electromagnetics, Ph.D. Thesis, McGill University, Montreal, Canada, 1985
I don’t think Robert would claim to be the earliest.
Then you can go back to 1976 with Józef Dodziuk’s classic paper:
- Finite difference approach to the Hodge theory of harmonic forms, Amer. J. Math., 98 (1976), 79-104.
Zoran: Surely, it is emphasised that the numerous precursors exist in the Bulletin survey of Douglas Arnold et al. quoted below. But it was not in any sense systematic till rather recently. One could expand on the history…
I have today posted a question to MathOverflow on recent-fundamental-new-directions-in-pdes.
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