Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

Cotter, Simon and Vejchodsky, Tomas and Erban, Radek (2013) Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems. SIAM Journal on Scientific Computing, 35 (1).

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Abstract

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.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Simon L Cotter
Date Deposited: 18 Dec 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2216

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