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Convergence analysis of sectional methods for solving breakage population balance equations-I: the fixed pivot technique

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Abstract

In this work we study the convergence of the fixed pivot techniques (Kumar and Ramkrishna Chem. Eng. Sci. 51, 1311–1332, 1996) for breakage problems. In particular, the convergence is investigated on four different types of uniform and non-uniform meshes. It is shown that the fixed pivot technique is second order convergent on a uniform and non-uniform smooth meshes. Furthermore, it gives first order convergence on a locally uniform mesh. Finally the analysis shows that the method does not converge on a non-uniform random mesh. The mathematical results of convergence analysis are also validated numerically.

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Authors and Affiliations

  1. Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Jitendra Kumar & Gerald Warnecke

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  1. Jitendra Kumar
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  2. Gerald Warnecke
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Correspondence to Jitendra Kumar.

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Kumar, J., Warnecke, G. Convergence analysis of sectional methods for solving breakage population balance equations-I: the fixed pivot technique. Numer. Math. 111, 81–108 (2008). https://doi.org/10.1007/s00211-008-0174-6

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  • DOI: https://doi.org/10.1007/s00211-008-0174-6

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