  A novel approach for the stabilization of the Discontinuous Galerkin method
based on the Dafermos entropy rate crition is presented. First, estimates for
the maximal possible entropy dissipation rate of a weak solution are derived.
Second, families of conservative Hilbert-Schmidt operators are identified to
dissipate entropy. Steering these operators using the bounds on the entropy
dissipation results in high-order accurate shock-capturing DG schemes for the
Euler equations, satisfying the entropy rate criterion and an entropy
inequality.
