Tone, F and Wang, XM and Wirosoetisno, D (2014) 'Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics.', Numerische mathematik., 130 (3). pp. 541-566.
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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1007/s00211-014-0670-9|
|Publisher statement:||The final publication is available at Springer via https://doi.org/10.1007/s00211-014-0670-9|
|Date accepted:||23 September 2014|
|Date deposited:||13 September 2017|
|Date of first online publication:||15 November 2014|
|Date first made open access:||No date available|
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