From June 11-15, 2012 I gave an intensive short course on Finite Element Exterior Calculus to an audience of nearly 70 faculty members, graduate students, and researchers from around the world. The course, which consisted of 10 lectures totaling about 15 hours, was held at the Institute for Computational & Experimental Research in Mathematics (ICERM) at Brown University. It was supported by the National Science Foundation (NSF) and the Conference Board of the Mathematical Sciences (CBMS).

• Course web page at ICERM
• Course slides
• Course video (hosted at ICERM)
  1. Introduction and motivations; Homology 101 (1:19)
  2. Homology continued; unbounded operators on Hilbert space (1:22)
  3. Hilbert complexes (1:55)
  4. The abstract Hodge Laplacian (1:26)
  5. Approximation of Hilbert complexes (1:43)
  6. Improved error estimates and eigenvalue problems; Exterior calculus (1:22)
  7. Finite element spaces of differential forms (1:21)
  8. Finite element spaces of differential forms, continued (1:11)
  9. Bounded cochain projections; Bases (1:33)
  10. Finite element differential forms on cubical meshes (0:58)
• The primary references for the course are these papers, couathored with R. Falk and R. Winther:
  • Finite element exterior calculus: from Hodge theory to numerical stability. BAMS, 47:281-354, 2010.
  • Finite element exterior calculus, homological techniques, and applications. Acta Numer., 15:1-155, 2006.
• Course photo