A 2D Cartesian electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) model presented previously (Liu et al 2018 Plasma Sources Sci. Technol. 27 025006) is used to investigate the effect of the driving frequency (over the range of 15?45 MHz) on the plasma uniformity in radio frequency (RF) capacitively coupled plasma (CCP) discharges in a geometrically symmetric reactor with a dielectric side wall in argon gas. The reactor size (12 cm electrode length, 2.5 cm gap) and driving frequency are sufficiently small that electromagnetic effects can be ignored. Previously, we showed (Liu et al 2018 Plasma Sources Sci. Technol. 27 025006) that for 15 MHz excitation, Ohmic heating of electrons by the electric field perpendicular to the electrodes is enhanced in a region in front of the dielectric side wall, leading to a maximum in electron density there. In this work we show that increasing the excitation frequency (at constant applied voltage amplitude) not only increases the overall electron heating and density but also causes a stronger, narrower peak in electron heating closer to the dielectric wall, improving the plasma uniformity along the electrodes. This heating peak comes both from enhanced perpendicular electron heating and from the appearance at high frequency of significant parallel heating. The latter is caused by the presence of a significant parallel-direction RF oscillating electric field in the corners. Whereas at the reactor center the sheaths oscillate perpendicularly to the electrodes, near the dielectric edge they move in and out of the corners and must be treated in two dimensions.