  Stochastic chemical systems with diffusion are modeled with a
reaction-diffusion master equation. On a macroscopic level, the governing
equation is a reaction-diffusion equation for the averages of the chemical
species. On a mesoscopic level, the master equation for a well stirred chemical
system is combined with Brownian motion in space to obtain the
reaction-diffusion master equation. The space is covered by an unstructured
mesh and the diffusion coefficients on the mesoscale are obtained from a finite
element discretization of the Laplace operator on the macroscale. The resulting
method is a flexible hybrid algorithm in that the diffusion can be handled
either on the meso- or on the macroscale level. The accuracy and the efficiency
of the method are illustrated in three numerical examples inspired by molecular
biology.
