Electron acceleration by large amplitude electrostatic waves in astrophysical plasmas is studied using particle-in-cell (PIC) simulations. The waves are excited initially at the electron plasma frequency $\omega_{\rm pe}$ by a Buneman instability driven by ion beams: the parameters of the ion beams are appropriate for high Mach number astrophysical shocks, such as those associated with supernova remnants (SNRs). If $\omega_{\rm pe}$ is much higher than the electron cyclotron frequency $\Omega_{\rm e}$, the linear phase of the instability does not depend on the magnitude of the magnetic field. However, the subsequent time evolution of particles and waves depends on both $\omega_{\rm pe}/\Omega_{\rm e}$ and the size of the simulation box $L$. If $L$ is equal to one wavelength, $\lambda_0$, of the Buneman-unstable mode, electrons trapped by the waves undergo acceleration via the surfatron mechanism across the wave front. This occurs most efficiently when $\omega_{\rm pe}/\Omega_{\rm e} \simeq 100$: in this case electrons are accelerated to speeds of up $c/2$ where $c$ is the speed of light. In a simulation with $L=4\lambda_0$ and $\omega_{\rm pe}/\Omega_{\rm e} = 100$, it is found that sideband instabilities give rise to a broad spectrum of wavenumbers, with a power law tail. Some stochastic electron acceleration is observed in this case, but not the surfatron process. Direct integration of the electron equations of motion, using parameters approximating to those of the wave modes observed in the simulations, suggests that the surfatron is compatible with the presence of a broad wave spectrum if $\omega_{\rm pe}/\Omega_{\rm e}> 100$. It is concluded that a combination of stochastic and surfatron acceleration could provide an efficient generator of mildly relativistic electrons at SNR shocks.