8 citations · 11 across the 15 of their papers we have counts for
5 papers · 1 filter
Towards finite element exterior calculus on manifolds: commuting projections, geometric variational crimes, and approximation errors
Martin W. Licht
We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differ…
Smoothed projections over manifolds in finite element exterior calculus
Martin W. Licht
We develop commuting finite element projections on compact Riemannian smooth manifolds. The commuting projections are constructed using localized smoothing operators, building on a…
Higher-order finite element de Rham complexes, partially localized flux reconstructions, and applications
Martin Werner Licht
We construct finite element de~Rham complexes of higher and possibly non-uniform polynomial order in finite element exterior calculus (FEEC). Starting from the finite element diffe…
Constructing collars in paracompact Hausdorff spaces and Lipschitz estimates
Martin Werner Licht
We give a constructive proof for the following new collar theorem: every locally collared closed set that is paracompact in a Hausdorff space is collared. This includes the importa…
Averaging-based local projections in finite element exterior calculus
Martin W. Licht
We construct local projection operators onto spaces of finite element differential forms on simplicial meshes. The projections are locally stable in Lebesgue and Sobolev--Slobodeck…