Finite element exterior calculus , homological techniques , and applications

  title={Finite element exterior calculus , homological techniques , and applications},
  author={Douglas N. Arnold and Richard S. Falk and Ragnar Winther},
Finite element exterior calculus is an approach to the design and understanding of finite element discretizations for a wide variety of systems of partial differential equations. This approach brings to bear tools from differential geometry, algebraic topology, and homological algebra to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the PDE problem being solved. In the finite element exterior calculus… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 80 references

Representation Theory, Vol. 129 of Graduate Texts

W. Fulton, J. Harris
View 6 Excerpts
Highly Influenced

Survey lectures on the mathematical foundations of the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

I. Babuška, A. K. Aziz
(Proc. Sympos., Univ. Maryland, • 1972
View 4 Excerpts
Highly Influenced

A posteriori error estimates for Maxwell equations

Math. Comput. • 2008
View 4 Excerpts
Highly Influenced

Fortin operator and discrete compactness for edge elements

Numerische Mathematik • 2000
View 5 Excerpts
Highly Influenced

Canonical construction of finite elements

Math. Comput. • 1999
View 5 Excerpts
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The mathematical theory of finite element methods, Vol. 15 of Texts in Applied Mathematics, second edn

S. C. Brenner, L. R. Scott
View 1 Excerpt
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