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On an Iterative Method for Approximate Solutions of a Generalized Boussinesq Model

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Abstract

An iterative method is proposed for finding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature dependent viscosity and thermal conductivity. Under certain conditions, it is proved that such approximate solutions converge to a solution of the original problem; moreover, convergence-rate bounds for the constructed approximate solutions are also obtained.

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Authors and Affiliations

  1. IMECC-UNICAMP, CP 6065, Campinas, 13083-859, SP, Brazil

    José Luiz Boldrini

  2. Dpto. de Ecuaciones Diferenciales y Análisis Numérico Facultad de Matemáticas, Universidad de Sevilla, 41012, Sevilla, Spain

    Blanca Climent-Ezquerra

  3. Dpto. de Matemática, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile

    María Drina Rojas-Medar

  4. Dpto. de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May Casilla 447, Chillán, Chile

    Marko A. Rojas-Medar

Authors
  1. José Luiz Boldrini
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  2. Blanca Climent-Ezquerra
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  3. María Drina Rojas-Medar
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  4. Marko A. Rojas-Medar
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Corresponding author

Correspondence to José Luiz Boldrini.

Additional information

Communicated by G. P. Galdi.

J.L. Boldrini, B. Climent-Ezquerra, M.A. Rojas-Medar are partially supported by project MTM2006-07932, Spain; M.D. Rojas-Medar is partially supported by Universidad de Antofagasta, Project PEI: 1333 and Fondecyt-Chile, Grant 1080628; J.L. Boldrini is also partially supported by CNPq-Brazil, Grant 307833/2008-9, and M.A. Rojas-Medar is also partially supported by project Fondecyt-Chile, Grant 1080628.

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Boldrini, J.L., Climent-Ezquerra, B., Rojas-Medar, M.D. et al. On an Iterative Method for Approximate Solutions of a Generalized Boussinesq Model. J. Math. Fluid Mech. 13, 33–53 (2011). https://doi.org/10.1007/s00021-009-0001-6

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  • DOI: https://doi.org/10.1007/s00021-009-0001-6

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