In some laboratory and most astrophysical situations plasma wake-field acceleration of electrons is one dimensional, i.e. variation transverse to the beams motion can be ignored. Thus, one dimensional (1D), particle-in-cell (PIC), fully electromagnetic simulations of electron plasma wake field acceleration are conducted in order to study the differences in electron plasma wake field acceleration in MeV versus GeV and linear versus blowout regimes. First, we show that caution needs to be taken when using fluid simulations, as PIC simulations prove that an approximation for an electron bunch not to evolve in time for few hundred plasma periods only applies when it is sufficiently relativistic. This conclusion is true irrespective of the plasma temperature. We find that in the linear regime and GeV energies, the accelerating electric field generated by the plasma wake is similar to the linear and MeV regime. However, because GeV energy driving bunch stays intact for much longer time, the final acceleration energies are much larger in the GeV energies case. In the GeV energy range and blowout regime the wakes accelerating electric field is much larger in amplitude compared to the linear case and also plasma wake geometrical size is much larger. Thus, the correct positioning of the trailing bunch is needed to achieve the efficient acceleration. For the considered case, optimally there should be approximately $(90-100) c/omega_{pe}$ distance between trailing and driving electron bunches in the GeV blowout regime.
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