homological algebra in the finite element method

Recently, homological algebra started appearing in the study of numerical stability for finite element methods,

- 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)

Revised on May 4, 2013 14:18:39
by Zoran Škoda
(37.244.145.187)