  A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous
Galerkin (HDG) discretizations based only on the HDG hybrid variable is
presented for linear thermal and elastic problems. The hybrid CG-HDG coupling
exploits the definition of the numerical flux and the trace of the solution on
the mesh faces to impose the transmission conditions between the CG and HDG
subdomains. The continuity of the solution is imposed in the CG problem via
Nitsche's method, whereas the equilibrium of the flux at the interface is
naturally enforced as a Neumann condition in the HDG global problem. The
proposed strategy does not affect the core structure of CG and HDG
discretizations. In fact, the resulting formulation leads to a
minimally-intrusive coupling, suitable to be integrated in existing CG and HDG
libraries. Numerical experiments in two and three dimensions show optimal
global convergence of the stress and superconvergence of the displacement
field, locking-free approximation, as well as the potential to treat structural
problems of engineering interest featuring multiple materials with compressible
and nearly incompressible behaviors.
