Geodesic
Convergence of the cell average technique for Smoluchowski coagulation equation
Giri, Ankik Kumar1, 2 ; Nagar, Atulya K.3
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.
3 Department of Mathematics and computer science, Liverpool Hope University, Hope Park, Liverpool, UK.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 349-372

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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.

Reçu le :
DOI : 10.1051/m2an/2014035
Classification : 45J05, 45K05, 45L05, 65R20
Keywords: Particles, coagulation, cell average technique, consistency, Lipschitz condition, convergence

Giri, Ankik Kumar 1, 2 ; Nagar, Atulya K. 3

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.
3 Department of Mathematics and computer science, Liverpool Hope University, Hope Park, Liverpool, UK. 
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     title = {Convergence of the cell average technique for {Smoluchowski} coagulation equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {349--372},
     publisher = {EDP-Sciences},
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Giri, Ankik Kumar; Nagar, Atulya K. Convergence of the cell average technique for Smoluchowski coagulation equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 349-372. doi: 10.1051/m2an/2014035

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