  We present unconditionally energy stable Runge-Kutta (RK) discontinuous
Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our
algorithm is geared toward arbitrarily high order approximations in both space
and time, while energy dissipation remains preserved without imposing any
restriction on time steps and meshes. We achieve this in two steps. First,
taking advantage of the penalty free DG method introduced by Liu and Yin [J
Sci. Comput. 77:467--501, 2018] for spatial discretization, we reformulate an
extended linearized ODE system by the energy quadratization (EQ) approach.
Second, we apply an s-stage algebraically stable RK method for temporal
discretization. The resulting fully discrete DG schemes are linear and
unconditionally energy stable. In addition, we introduce a
prediction-correction procedure to improve both the accuracy and stability of
the scheme. We illustrate the effectiveness of the proposed schemes by
numerical tests with benchmark problems.
