We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.
|Original language||English (US)|
|Title of host publication||Springer INdAM Series|
|Publisher||Springer International Publishing|
|Number of pages||24|
|State||Published - 2013|
|Name||Springer INdAM Series|
Bibliographical noteFunding Information:
The work of the author was supported by NSF grant DMS-1115291.