  We propose a new Lagrange Multiplier approach to design unconditional energy
stable schemes for gradient flows. The new approach leads to unconditionally
energy stable schemes that are as accurate and efficient as the recently
proposed SAV approach \cite{SAV01}, but enjoys two additional advantages: (i)
schemes based on the new approach dissipate the original energy, as opposed to
a modified energy in the recently proposed SAV approach \cite{SAV01}; and (ii)
they do not require the nonlinear part of the free energy to be bounded from
below as is required in the SAV approach. The price we pay for these advantages
is that a nonlinear algebraic equation has to be solved to determine the
Lagrange multiplier. We present ample numerical results to validate the new
approach, and, as a particular example of applications, we consider a coupled
Cahn-Hilliard model for block copolymers (BCP), and carry out interesting
simulations which are consistent with experiment results.
