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We give some theoretical as well as computational results on Laplace andMaxwell constants. Besides the classical de Rham complex we investigate thecomplex of elasticity and the complex related to the biharmonic equation andgeneral relativity as well using the general functional analytical concept ofHilbert complexes. We consider mixed boundary conditions and bounded Lipschitzdomains of arbitrary topology. Our numerical aspects are presented by examplesfor the de Rham complex in 2D and 3D which not only confirm our theoreticalfindings but also indicate some interesting conjectures.

Poincare-Friedrichs Type Constants for Operators Involving grad, curl, and div: Theory and Numerical Experiments