  We analyze minimizers of the Lawrence-Doniach energy for layered
superconductors occupying a bounded generalized cylinder, $ \Omega\times[0,L]$,
in $\mathbb{R}^3$, where $\Omega$ is a bounded simply connected Lipschitz
domain in $\mathbb{R}^2$. For an applied magnetic field
$\vec{H}_{ex}=h_{ex}\vec{e}_{3}$ that is perpendicular to the layers with
$\left|\ln\epsilon\right|\ll h_{ex}\ll\epsilon^{-2}$ as $\epsilon\rightarrow
0$, where $\epsilon$ is the reciprocal of the Ginzburg-Landau parameter, we
prove an asymptotic formula for the minimum Lawrence-Doniach energy as
$\epsilon$ and the interlayer distance $s$ tend to zero. Under appropriate
assumptions on $s$ versus $\epsilon$, we establish comparison results between
the minimum Lawrence-Doniach energy and the minimum three-dimensional
anisotropic Ginzburg-Landau energy. As a consequence, our asymptotic formula
also describes the minimum three-dimensional anisotropic energy as $\epsilon$
tends to zero.
