nLab
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)