Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics | Zendy

Florentina Tone | Zendy; Xiaoming Wang | Zendy; D. Wirosoetisno | Zendy

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Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics

Author(s) -

Florentina Tone,

Xiaoming Wang,

D. Wirosoetisno

Publication year - 2014

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/s00211-014-0670-9

Subject(s) - mathematics , discretization , attractor , convergence (economics) , time derivative , limit (mathematics) , discrete time and continuous time , invariant (physics) , mathematical analysis , term (time) , statistical physics , statistics , physics , economics , mathematical physics , economic growth , quantum mechanics

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. As a consequence, the convergence of the attractors and long time statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods

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