We present a fully ab initio, nonperturbative, time-dependent approach to describe single and double ionization of helium by proton and antiproton impact. The problem is discretized by a flexible finite-element discrete-variable representation on the radial grid. Good agreement with the most recent experimental data for absolute angle-integrated cross sections is obtained for projectile energies between 3 keV and 6 MeV. Also, angle-differential cross sections for two-electron ejection are predicted for a proton impact energy of 6 MeV. The time evaluation of the ionization process is portrayed by displaying the electron density as a function of the projectile location.