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All issues Volume 55 / No 6 (November-December 2021) ESAIM: M2AN, 55 6 (2021) 3043-3089 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
Page(s) 3043 - 3089
DOI https://doi.org/10.1051/m2an/2021079
Published online 17 December 2021
  1. R.A. Adams, Sobolev Spaces. Pure and Applied Mathematics. Vol. 65, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1975). [Google Scholar]
  2. A. Ait Hammou Oulhaj, C. Cancès and C. Chainais-Hillairet, Numerical analysis of a nonlinearly stable and positive control volume finite element scheme for Richards equation with anisotropy. ESAIM: M2AN 52 (2018) 1533–1567. [CrossRef] [EDP Sciences] [Google Scholar]
  3. P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre, J.L. Vázquez, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995) 241–273. [MathSciNet] [Google Scholar]
  4. L. Boccardo and T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989) 149–169. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Boccardo, T. Gallouët and J.L. Vázquez, Nonlinear elliptic equations in RN without growth restrictions on the data. J. Differ. Equ. 105 (1993) 334–363. [CrossRef] [Google Scholar]
  6. C. Cancès and C. Guichard, Convergence of a nonlinear entropy diminishing control volume finite element scheme for solving anisotropic degenerate parabolic equations. Math. Comp. 85 (2016) 549–580. [Google Scholar]
  7. C. Cancès, M. Ibrahim and M. Saad, Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system. SMAI J. Comput. Math. 3 (2017) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Casado-Daz, T. Chacón Rebollo, V. Girault, M. Gómez Mármol and F. Murat, Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in L1. Numer. Math. 105 (2007) 337–374. [Google Scholar]
  9. P.G. Ciarlet, The finite element method for elliptic problems. In: Studies in Mathematics and its Applications. Vol. 4. North-Holland Publishing Co., Amsterdam-New York-Oxford (1978) xix+530. [Google Scholar]
  10. G. Dal Maso, F. Murat, L. Orsina and A. Prignet, Renormalized solutions of elliptic equations with general measure data. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999) 741–808. [MathSciNet] [Google Scholar]
  11. A. Dall’Aglio, A remark on the entropy solutions. Personal Communication (1996). [Google Scholar]
  12. K. Deimling, Nonlinear Functional Analysis. Springer-Verlag, Berlin (1985). [Google Scholar]
  13. J. Droniou, Solving convection-diffusion equations with mixed, neumann and fourier boundary conditions and measures as data, by a duality method. Adv. Differ. Equ. 5 (2000) 1341–1396. [Google Scholar]
  14. J. Droniou, Non-coercive linear elliptic problems. Potential Anal. 17 (2002) 181–203. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Droniou, T. Gallouët and R. Herbin, A finite volume scheme for a noncoercive elliptic equation with measure data. SIAM J. Numer. Anal. 41 (2003) 1997–2031. [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Ern and J.-L. Guermond, Applied Mathematical Sciences. Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  17. R. Eymard, T. Gallouët and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces. IMA J. Numer. Anal. 30 (2010) 1009–1043. [CrossRef] [MathSciNet] [Google Scholar]
  18. R. Eymard, T. Gallouët, C. Guichard, R. Herbin and R. Masson, TP or not TP, that is the question. Comput. Geosci. 18 (2014) 285–296. [Google Scholar]
  19. P. Fabrie and T. Gallouët, Modelling wells in porous media flow. Math. Models Methods Appl. Sci. 10 (2000) 673–709. [CrossRef] [MathSciNet] [Google Scholar]
  20. T. Gallouët and R. Herbin, Existence of a solution to a coupled elliptic system. Appl. Math. Lett. 7 (1994) 49–55. [CrossRef] [MathSciNet] [Google Scholar]
  21. T. Gallouët and A. Monier, On the regularity of solutions to elliptic equations. Rend. Mat. Appl. 19 (1999) 471–488. [MathSciNet] [Google Scholar]
  22. N.G. Meyers, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1963) 189–206. [MathSciNet] [Google Scholar]
  23. A. Prignet, Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures. Rend. Mat. Appl. 15 (1995) 321–337. [MathSciNet] [Google Scholar]
  24. J. Serrin, Pathological solutions of elliptic differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964) 385–387. [Google Scholar]
  25. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. [CrossRef] [MathSciNet] [Google Scholar]

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