# Finite element exterior calculus , homological techniques , and applications

@inproceedings{Arnold2006FiniteEE, title={Finite element exterior calculus , homological techniques , and applications}, author={Douglas N. Arnold and Richard S. Falk and Ragnar Winther}, year={2006} }

- Published 2006

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

#### From This Paper

##### Figures, tables, and topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-10 of 246 extracted citations

## Computation and Visualization of Geometric Partial Differential Equations

View 17 Excerpts

Highly Influenced

## Finite Element Exterior Calculus for Parabolic Evolution Problems on Riemannian Hypersurfaces

View 15 Excerpts

Highly Influenced

## Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

View 20 Excerpts

Highly Influenced

## Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data ∗

View 14 Excerpts

Highly Influenced

## MultiGrid Preconditioners for Mixed Finite Element Methods of the Vector Laplacian

View 6 Excerpts

Highly Influenced

## Complexes of Discrete Distributional Differential Forms and Their Homology Theory

View 7 Excerpts

Highly Influenced

## On high order finite element spaces of differential forms

View 9 Excerpts

Highly Influenced

## A finite element exterior calculus framework for the rotating shallow-water equations

View 7 Excerpts

Highly Influenced

## Geometric Variational Crimes: Hilbert Complexes, Finite Element Exterior Calculus, and Problems on Hypersurfaces

View 4 Excerpts

Highly Influenced

#### Citation Statistics

#### 428 Citations

Citations per Year

Semantic Scholar estimates that this publication has

**428**citations based on the available data.See our **FAQ** for additional information.

#### References

##### Publications referenced by this paper.

Showing 1-10 of 80 references

## Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension

View 12 Excerpts

Highly Influenced

## Representation Theory, Vol. 129 of Graduate Texts

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

View 4 Excerpts

Highly Influenced

## A posteriori error estimates for Maxwell equations

View 4 Excerpts

Highly Influenced

## Fortin operator and discrete compactness for edge elements

View 5 Excerpts

Highly Influenced

## Canonical construction of finite elements

View 5 Excerpts

Highly Influenced

## Multigrid Method for H(div) in Three Dimensions

View 4 Excerpts

Highly Influenced

## Multigrid Methods for Maxwell's Equations List of Tables

View 5 Excerpts

Highly Influenced

## The mathematical theory of finite element methods, Vol. 15 of Texts in Applied Mathematics, second edn

View 1 Excerpt

Highly Influenced

## Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domains

View 1 Excerpt

Highly Influenced