We present a general framework for the numerical resolution of processes
driven by geometric components such as the curvature of the domain boundary.
In this context, the Laplace-Beltrami operator plays a crucial role.
Two applications are discussed: Electrowetting on dielectric (EWOD) and
the simulation of Biomembranes.
The former refers to a parallel-plate
micro-device that moves fluid droplets through electrically
actuated surface tension effects. These devices have potential