  The emission mechanism for hard $\gamma$-ray spectra from supernova remnants
(SNRs) is still a matter of debate. Recent multi-wavelength observations of TeV
source HESS J1912+101 show that it is associated with an SNR with an age of
$\sim 100$ kyrs, making it unlikely produce the TeV $\gamma$-ray emission via
leptonic processes. We analyzed Fermi observations of it and found an extended
source with a hard spectrum. HESS J1912+101 may represent a peculiar stage of
SNR evolution that dominates the acceleration of TeV cosmic rays. By fitting
the multi-wavelength spectra of 13 SNRs with hard GeV $\gamma$-ray spectra with
simple emission models with a density ratio of GeV electrons to protons of
$\sim 10^{-2}$, we obtain reasonable mean densities and magnetic fields with a
total energy of $\sim 10^{50}$ ergs for relativistic ions in each SNR. Among
these sources, only two of them, namely SN 1006 and RCW 86, favor a leptonic
origin for the $\gamma$-ray emission. The magnetic field energy is found to be
comparable to that of the accelerated relativistic ions and their ratio has a
tendency of increase with the age of SNRs. These results suggest that TeV
cosmic rays mainly originate from SNRs with hard $\gamma$-ray spectra.
