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 longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.
F. Tone et al., "Long-Time Dynamics of 2d Double-Diffusive Convection: Analysis And/of Numerics," Numerische Mathematik, vol. 130, no. 3, pp. 541 - 566, Springer, Jul 2015.
The definitive version is available at https://doi.org/10.1007/s00211-014-0670-9
Mathematics and Statistics
Keywords and Phrases
35B35; 35K45; 65M12
International Standard Serial Number (ISSN)
Article - Journal
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28 Jul 2015