How does energy get transferred from the inductor to capacitor in the LC circuit?

Just as energy is stored in the magnetic field induced by a current through an inductor (see question above, $U = \frac{1}{2 \mu_0} \int \vec{B}^2 dV$), energy is stored in the electric field between a capacitor's plates, $U =\frac{1}{2} \epsilon \int \vec{E}^2 dV$. The energy stored in the magnetic field induced by the current through the inductor gets transformed into energy stored in the electric field of the capactor, as the capacitor charges up and the current decreases (capacitor electric field increases as inductor magnetic field decreases, and vice versa).