Cotter, S. L. and Vejchodsky, T. and Erban, R. (2011) *Adaptive finite element method assisted by stochastic simulation of chemical systems.* SIAM Journal on Scientific Computing . (Submitted)

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## Abstract

Stochastic models of chemical systems are often analysed 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 non-negligible 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 probability density.

Item Type: | Article |
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Subjects: | D - G > General |

Research Groups: | Oxford Centre for Collaborative Applied Mathematics |

ID Code: | 1467 |

Deposited By: | Peter Hudston |

Deposited On: | 22 Feb 2012 07:53 |

Last Modified: | 22 Feb 2012 07:53 |

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