Convergence of the cell average technique for Smoluchowski coagulation equation
1 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India.
2 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria.
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3 Department of Mathematics and computer science, Liverpool Hope University, Hope Park, Liverpool, UK.
Received: 15 December 2012
Revised: 19 March 2014
We present the convergence analysis of the cell average technique, introduced in [J. Kumar et al., Powder Technol. 179 (2007) 205–228.], to solve the nonlinear continuous Smoluchowski coagulation equation. It is shown that the technique is second order accurate on uniform grids and first order accurate on non-uniform smooth (geometric) grids. As an essential ingredient, the consistency of the technique is thoroughly discussed.
Mathematics Subject Classification: 45J05 / 45K05 / 45L05 / 65R20
Key words: Particles / coagulation / cell average technique / consistency / Lipschitz condition / convergence
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