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H1-conforming finite element cochain complexes and commuting quasi-interpolation operators on cartesian meshes (2010.00524v1)
Published 1 Oct 2020 in math.NA and cs.NA
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.