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Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem

Abstract

We first summarize the general concept of our verification method of solutions for elliptic equations. Next, as an application of our method, a survey and future works on the numerical verification method of solutions for heat convection problems known as Rayleigh-Bénard problem are described. We will give a method to verify the existence of bifurcating solutions of the two-dimensional problem and the bifurcation point itself. Finally, an extension to the three-dimensional case and future works will be described.

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Correspondence to Yoshitaka Watanabe.

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Watanabe, Y., Nakao, M.T. Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. Japan J. Indust. Appl. Math. 26, 443–463 (2009). https://doi.org/10.1007/BF03186543

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  • DOI: https://doi.org/10.1007/BF03186543

Key words

  • numerical verification method
  • elliptic equations
  • Rayleigh-Bénard problem
  • bifurcation point