You are here: MIMS > EPrints
MIMS EPrints

2014.72: Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

2014.72: Simon Cotter, Tomas Vejchodsky and Radek Erban (2013) Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems. SIAM Journal on Scientific Computing, 35 (1).

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
1117 Kb

DOI: 10.1137/120877374

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 2000 > 65 Numerical analysis
MIMS number:2014.72
Deposited By:Dr Simon L Cotter
Deposited On:18 December 2014

Download Statistics: last 4 weeks
Repository Staff Only: edit this item