The {it Fermi} Large Area Telescope has recently discovered two giant gamma-ray bubbles which extend north and south of the Galactic center with diameters and heights of the order of $Hsim 10$ kpc. We suggest that the periodic star capture processes by the Galactic supermassive black hole Sgr A$^*$, with a capture rate of $tau_{rm cap}^{-1}sim 3times 10^{-5}$ yr$^{-1}$ and an energy release of $Wsim 3times 10^{52}$ erg per capture, can result in hot plasma injecting into the Galactic halo at a wind velocity of $usim 10^8$ cm s$^{-1}$. The periodic injection of hot plasma can produce a series of shocks. Energetic protons in the bubble are re-accelerated when they interact with these shocks. We show that for energy larger than $E> 10^{15}$ eV, the acceleration process can be better described by the stochastic second-order Fermi acceleration. We propose that hadronic cosmic rays (CRs) within the ``knee of the observed CR spectrum are produced by Galactic supernova remnants distributed in the Galactic disk. Re-acceleration of these particles in the Fermi Bubble produces CRs beyond the knee. With a mean CR diffusion coefficient in this energy range in the bubble $D_Bsim 3times 10^{30}$ cm$^2$ s$^{-1}$, we can reproduce the spectral index of the spectrum beyond the knee and within. The conversion efficiency from shock energy of the bubble into CR energy is about 10%. This model provides a natural explanation of the observed CR flux, spectral indices, and matching of spectra at the knee.
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