Smoothed projections in finite element exterior calculus

The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are L2 bounded projections, and still they commute with the exterior derivative. In the present paper we generalize the construction of these smoothed projections, such that also non-quasi-uniform meshes and essential boundary conditions are covered. The new tool introduced here is a space-dependent smoothing operator that commutes with the exterior derivative.