Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

Simon L. Cotter, Tomáš Vejchodský, Radek Erban

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)B107-B131
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - Jan 2013
Externally publishedYes


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