The electron power absorption dynamics and plasma uniformity in low pressure capacitively coupled RF discharges with structured electrodes are investigated by graphics processing unit-based 2d3v particle-in-cell/Monte Carlo simulations in argon gas. In the presence of planar electrodes, the plasma is radially nonuniform due to strong electron density peaks close to the reactor sidewall, which are caused by edge effects that locally enhance the electron power absorption and ionization. Such a local enhancement of these characteristics can also be achieved in a controllable manner by using a single ring-shaped rectangular trench embedded in the powered electrode close to the reactor center. This effect is understood by analyzing the trajectories of selected electrons as well as the time evolution of their energy and velocity inside and above such trenches. Electrons are found to gain high energies inside the trench by bouncing between the sheaths at the trench walls during the sheath expansion phase. Combined with the cross-firing of energetic electrons at the trench orifice, this leads to high local ionization rates. Using these trench effects, the plasma uniformity above the wafer placed on a planar powered electrode can be remarkably improved by including multiple trenches in the opposing grounded electrode, which enhance the ionization and plasma density at their respective radial positions. Meanwhile, the ion flux-energy distribution function at the wafer is found to be almost unaffected.