Abstract
In this work, we apply a method due to De Giorgi [3] in order to establish a positive lower bound for the numerical solution of a stationary convection-diffusion equation.
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References
Bessemoulin-Chatard, M., Chainais-Hillairet, C., Filbet, F.: On discrete functional inequalities for some finite volume schemes. IMA J. Numer. Anal, 10–32 (2014)
Chainais-Hillairet, C., Gisclon, M., Jüngel, A.: A finite-volume scheme for the multidimensional quantum drift-diffusion model for semiconductors. Numer. Methods Partial Differ. Equ. 27(6), 1483–1510 (2011)
De Giorgi, E.: Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari. Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. 3(3), 25–43 (1957)
Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Handbook of Numerical Analysis, vol. VII, pp. 713–1020. North-Holland, Amsterdam (2000)
Vasseur, A.F.: The De Giorgi method for elliptic and parabolic equations and some applications. In: Lectures on the analysis of nonlinear partial differential equations. Part 4, Morningside Lect. Math. vol. 4, pp. 195–222. Int. Press, Somerville, MA (2016)
Ziemer, W.P.: Weakly Differentiable Functions. Graduate Texts in Mathematics, vol. 120. Springer, New York (1989)
Acknowledgements
C. C.-H. and B. M. thank the team Inria/Rapsodi and the Labex CEMPI (ANR-11-LABX-0007-01) for their support. The authors thank the referees for their careful reading.
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Chainais-Hillairet, C., Merlet, B., Vasseur, A.F. (2017). Positive Lower Bound for the Numerical Solution of a Convection-Diffusion Equation . In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_26
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DOI: https://doi.org/10.1007/978-3-319-57397-7_26
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