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Finite Volume Scheme and Renormalized Solutions for a Noncoercive Elliptic Problem with L1 Data

  • Sarah Leclavier EMAIL logo

Abstract

The paper proves the convergence of the finite volume approximate solution of a convection-diffusion equation with an L1 right-hand side to the unique renormalized solution. The main difficulties are to handle the noncoercive character of the operator and the L1 data. Mixing the techniques of renormalized solutions and the finite volume method allows one to derive estimates for the discrete solutions and in particular a discrete version of the decay of the truncated energy. Indeed, as in the continuous case, the decay of the truncated energy is crucial to show that the limit of the approximate solution is the renormalized solution.

MSC 2010: 65N12; 35G15

Acknowledgements

The author wishes to thank O. Guibé for his precious help and the two anonymous referees for their valuable remarks.

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Received: 2016-5-26
Revised: 2016-9-25
Accepted: 2016-10-19
Published Online: 2016-11-8
Published in Print: 2017-1-1

© 2017 by De Gruyter

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