Switching of pixels in surface-stabilized ferroelectric liquid crystal cells is studied. We have performed numerical calculations in two spatial dimensions on an adaptive grid to determine solutions for the scalar fields of the director twist angle and the electric potential. In the bulk we employ the full Frank-Oseen energy (i.e. no one-constant approximation) with the addition of electric terms represented by a uniaxial dielectric tensor and the spontaneous polarization. On the surface the director is anchored by a Rapini-Papoular potential. An idealized bookshelf-configuration with fixed tilt angle of the director is assumed. During both switching on and off disclination pairs are created on the surface. These disclinations form the ends of Bloch walls which bound the pixel. In the range of medium voltages after switching on an internal wall remains within the pixel which leads to an inhomogeneous director field and complicates switching off.