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

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

2010-07-07

arxiv.org/abs/1007.1120v1

Numerische Mathematik, Vol. 107, No. 1, p. 87-106, 2007

Mathematics

Numerical Analysis

26 pages

Scientific paper

10.1007/s00211-007-0081-2

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological properties. The analysis applies in particular to certain $hp$ finite element spaces, extending results in trivial topology often referred to as the exact sequence property. Then we define regularization operators. Combined with the standard interpolators they enable us to prove discrete Poincar\'e-Friedrichs inequalities and discrete Rellich compactness for finite element spaces of differential forms of arbitrary degree on compact manifolds of arbitrary dimension.

Affiliated with

Also associated with

No associations

Rating

Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension 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 Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-345388