As described previously, continuum models, such as the Smoluchowski equation, offer a scalable framework for studying diffusion in biomolecular systems. This work presents new developments in the efficient solution of the continuum diffusion equation. Specifically, we present methods for adaptively refining finite element solutions of the Smoluchowski equation based on a posteriori error estimates. We also describe new, molecular-surface-based models, for diffusional reaction boundary criteria and compare results obtained from these models with the traditional spherical criteria. The new methods are validated by comparison of the calculated reaction rates with experimental values for wild-type and mutant forms of mouse acetylcholinesterase. The results show good agreement with experiment and help to define optimal reactive boundary conditions.