Adaptive finite element method assisted by stochastic simulation of chemical systems

0391351 - MÚ 2014 RIV US eng J - Journal Article
Cotter, S.L. - Vejchodský, Tomáš - Erban, R.
Adaptive finite element method assisted by stochastic simulation of chemical systems.
SIAM Journal on Scientific Computing. Roč. 35, č. 1 (2013), B107-B131. ISSN 1064-8275. E-ISSN 1095-7197
R&D Projects: GA AV ČR(CZ) IAA100190803
Institutional support: RVO:67985840
Keywords : chemical Fokker-Planck * adaptive meshes * stochastic simulation algorithm
Subject RIV: BA - General Mathematics
Impact factor: 1.940, year: 2013
http://epubs.siam.org/doi/abs/10.1137/120877374

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.
Permanent Link: http://hdl.handle.net/11104/0220438