Local bounded cochain projection
Provides a locally defined projection operator for finite element exterior calculus, addressing a known bottleneck in constructing stable and local projections for high-order differential forms.
This paper constructs local bounded cochain projections from L2 differential forms to finite-dimensional piecewise polynomial subspaces on simplicial meshes, achieving commutativity with the exterior derivative and mesh-independent boundedness.
We construct projections from the space of differential k-forms which belong to L2 and whose exterior derivative also belongs to L2, to finite dimensional subspaces of piecewise polynomial differential forms defined on a simplicial mesh. These projections have the properties that they commute with the exterior derivative and are bounded independent of the mesh size. Unlike some other recent work in this direction, the projections are also locally defined in the sense that they are defined by local operators on overlapping macroelements, in the spirit of the Clement interpolant.