  We consider the numerical solution of coupled volume-surface
reaction-diffusion systems having a detailed balance equilibrium. Based on the
conservation of mass, an appropriate quadratic entropy functional is identified
and an entropy-entropy dissipation inequality is proven. This allows us to show
exponential convergence to equilibrium by the entropy method. We then
investigate the discretization of the system by a finite element method and an
implicit time stepping scheme including the domain approximation by polyhedral
meshes. Mass conservation and exponential convergence to equilibrium are
established on the discrete level by arguments similar to those on the
continuous level and we obtain estimates of optimal order for the
discretization error which hold uniformly in time. Some numerical tests are
presented to illustrate these theoretical results. The analysis and the
numerical approximation are discussed in detail for a simple model problem. The
basic arguments however apply also in a more general context. This is
demonstrated by investigation of a particular volume-surface reaction-diffusion
system arising as a mathematical model for asymmetric stem cell division.
