The Mathematical Institute, University of Oxford, Eprints Archive

Adaptive finite element method assisted by stochastic simulation of chemical systems

Cotter, S L and Vejchodsky, T. and Erban, R. (2013) Adaptive finite element method assisted by stochastic simulation of chemical systems. Siam Journal on Scientific Computing, 35 (1). B107-B131.

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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:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1794
Deposited By: Sara Jolliffe
Deposited On:16 Feb 2014 09:26
Last Modified:29 May 2015 19:29

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