Abstract
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.
Recommended Citation
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
Department(s)
Mathematics and Statistics
Keywords and Phrases
35B35; 35K45; 65M12
International Standard Serial Number (ISSN)
0029-599X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Springer, All rights reserved.
Publication Date
28 Jul 2015
Comments
National Science Foundation, Grant None