Finite element systems of differential forms

Details Finite element systems of differential forms Finite element systems of differential forms

2010-06-24

arxiv.org/abs/1006.4779v2

Mathematics

Numerical Analysis

This draft has been withdrawn by the author because the extended version has been published as part of a paper with several co

Scientific paper

We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance composite piecewise polynomials finite elements of variable order over polyhedral grids. Under natural algebraic and metric conditions, interpolators and smoothers are constructed, which commute with the exterior derivative and whose product is uniformly stable in Lebesgue spaces. As a consequence we obtain not only eigenpair approximation for the Hodge-Laplacian in mixed form, but also variants of Sobolev injections and translation estimates adapted to variational discretizations.

Affiliated with

Also associated with

No associations

Rating

Finite element systems of differential forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite element systems of differential forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite element systems of differential forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675900