Calcium is an important second messenger in cell communication. The dynamics of intracellular calcium is determined by the liberation and uptake by cellular stores and reactions with buffers. We develop models and numerical tools to study the liberation of calcium from the endoplasmic reticulum. This process is characterized by the existence of multiple length scales. Local events, Ca2+ puffs at length scales of nanometers, originate at clusters of the inositol-1,4,5 trisphosphate (IP3) receptor channels. The interaction of these local stochastic events leads to Ca2+ waves, typically of micrometer size, which travel through the whole cell. We use a finite-element software package to implement the reaction-diffusion processes for concentration fields of Ca2+ and buffer proteins. In our description the dynamics of IP3-controlled channels remains discrete and stochastic and is implemented in the numerical simulations by a stochastic source term in the reaction diffusion equation. The strongly localized temporal behavior due to the on-off behavior of channels as well as their spatial localization is treated by an adaptive numerical method. We characterize phenomena such as nucleation and pinning of waves.