Open Access
Volume 55, Number 4, July-August 2021
Page(s) 1405 - 1437
Published online 13 July 2021
  1. D. Boffi, F. Brezzi and F. Michel, Mixed Finite Element Methods and Applications. In: Vol. 44 of Series in Computational Mathematics. Springer (2013). [Google Scholar]
  2. F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier–Stokes Equations and Related Models. In: Vol. 183 of Applied Mathematical Sciences (Switzerland). Springer (2013). [CrossRef] [Google Scholar]
  3. H.M. Byrne and L. Preziosi, Modelling solid tumour growth using the theory of mixtures. Math. Med. Biol. 20 (2003) 341–366. [CrossRef] [PubMed] [Google Scholar]
  4. C. Chainais-Hillairet, Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate. ESAIM: M2AN 33 (1999) 129–156. [CrossRef] [EDP Sciences] [Google Scholar]
  5. S. Champier, T. Gallouët and R. Herbin, Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh. Numer. Math. 66 (1993) 139–157. [CrossRef] [MathSciNet] [Google Scholar]
  6. B. Cockburn, P.A. Gremaud and J.X. Yang, A priori error estimates for numerical methods for scalar conservation laws part III: multidimensional flux-splitting monotone schemes on non-Cartesian grids. SIAM J. Numer. Anal. 35 (1998) 1775–1803. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Conway and J. Smoller, Global solutions of the cauchy problem for quasi-linear first-order equations in several space variables. Commun. Pure Appl. Math. 19 (1966) 95–105. [Google Scholar]
  8. M.G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws. Math. Comput. 34 (1980) 1–21. [Google Scholar]
  9. B. Després, An explicit a priori estimate for a finite volume approximation of linear advection on non-Cartesian grids. SIAM J. Numer. Anal. 42 (2005) 484–504. [Google Scholar]
  10. R.J. DiPerna and P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511–547. [Google Scholar]
  11. J. Droniou, R. Eymard, T. Gallouët, C. Guichard and R. Herbin, The Gradient Discretisation Method. In: Vol. 82 of Mathematics & Applications. Springer (2018). [CrossRef] [Google Scholar]
  12. J. Droniou, N. Nataraj and G.C. Remesan, Convergence analysis of a numerical scheme for a tumour growth model (2019). [Google Scholar]
  13. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press Inc., Florida (2015). [Google Scholar]
  14. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, edited by P.G. Ciarlet and J.L. Lions. In: Vol. 7 of Solution of Equation in Rn (Part 3), Techniques of Scientific Computing (Part 3). Elsevier, Amsterdam (2000) 713–1018. [Google Scholar]
  15. S.J. Franks, H.M. Byrne, J.R. King, J.C.E. Underwood and C.E. Lewis, Modelling the early growth of ductal carcinoma in situ of the breast. J. Math. Biol. 47 (2003) 424–452. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  16. H. Holden and N.H. Risebro, Front Tracking for Hyperbolic Conservation Laws. Springer-Verlag, Berlin Heidelberg (2015). [Google Scholar]
  17. K.H. Karlsen and J.D. Towers, Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Adv. Appl. Math. Mech. 9 (2017) 515–542. [Google Scholar]
  18. N.N. Kuznetsov, Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation. USSR Comput. Math. Math. Phys. 16 (1976) 105–119. [Google Scholar]
  19. V.G. Maz’ya and J. Rossmann, Mathematical Surveys and Monographs. American Mathematical Society (2010). [Google Scholar]
  20. B. Merlet, L- and L2-error estimates for a finite volume approximation of linear advection. SIAM J. Numer. Anal. 46 (2007) 124–150. [Google Scholar]
  21. B. Merlet and J. Vovelle, Error estimate for finite volume scheme. Numer. Math. 106 (2007) 129–155. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Sanders, On convergence of monotone finite difference schemes with variable spatial differencing. Math. Comput. 40 (1983) 91–106. [CrossRef] [MathSciNet] [Google Scholar]

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