Résumé
In this work we address the reduction of face degrees of freedom (DOFs) for
discrete elasticity complexes. Specifically, using serendipity techniques, we
develop a reduced version of a recently introduced two-dimensional complex
arising from traces of the three-dimensional elasticity complex. The keystone
of the reduction process is a new estimate of symmetric tensor-valued
polynomial fields in terms of boundary values, completed with suitable
projections of internal values for higher degrees. We prove an extensive set of
new results for the original complex and show that the reduced complex has the
same homological and analytical properties as the original one. This paper also
contains an appendix with proofs of general Poincaré--Korn-type inequalities
for hybrid fields.