H1-conforming finite element cochain complexes and commuting quasi-interpolation operators on cartesian meshes
arXiv:2010.00524 · doi:10.1007/s10092-021-00409-6
Abstract
A finite element cochain complex on Cartesian meshes of any dimension based on the H1-inner product is introduced. It yields H1-conforming finite element spaces with exterior derivatives in H1. We use a tensor product construction to obtain L2-stable projectors into these spaces which commute with the exterior derivative. The finite element complex is generalized to a family of arbitrary order.