Free Access
Volume 49, Number 2, March-April 2015
Page(s) 529 - 550
Published online 17 March 2015
  1. Y. Achdou, C. Japhet, Y. Maday and F. Nataf, A new cement to glue non-conforming grids with Robin interface conditions: the finite volume case. Numer. Math. 92 (2002) 593–620. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutière, P.A. Raviart and N. Seguin, Relaxation methods and coupling procedures. Int. J. Numer. Methods Fluids 56 (2008) 1123–1129. [CrossRef] [Google Scholar]
  3. B. Andreianov, F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Numer. Method Partial Differ. Eq. 23 (2007) 145–195. [Google Scholar]
  4. B. Andreianov, M. Bendahmane and R. Ruiz Baier, Analysis of a finite volume method for a cross-diffusion model in population dynamics. Math. Meth. Appl. Sci. 21 (2011) 307–344. [CrossRef] [Google Scholar]
  5. M. Bessemoulin-Chatard, C. Chainais-Hillairet and F. Filbet, On discrete functional inequalities for some finite volume schemes. To appear in IMA J. Numer. Anal. (2014). [Google Scholar]
  6. P.J. Blanco, R.A. Feijóo and S.A. Urquiza, A unified variational approach for coupling 3D-1D models and its blood flow applications. Comput. Methods Appl. Mech. Eng. 196 (2007) 4391–4410. [CrossRef] [MathSciNet] [Google Scholar]
  7. P.J. Blanco, J.S. Leiva, R.A. Feijóo and G.S. Buscaglia, Black-box decomposition approach for computational hemodynamics: One-dimensional models. Comput. Methods Appl. Mech. Eng. 200 (2011) 1389–1405. [CrossRef] [Google Scholar]
  8. P.J. Blanco, M.R. Pivello, S.A. Urquiza and R.A. Feijóo, On the potentialities of 3D-1D coupled models in hemodynamics simulations. J. Biomech. 42 (2009) 919–930. [CrossRef] [PubMed] [Google Scholar]
  9. P.J. Blanco, S.A. Urquiza and R.A. Feijóo, Assessing the influence of heart rate in local hemodynamics through coupled 3D-1D-0D models. Int. J. Numer. Methods Biomed. Eng. 26 (2010) 890–903. [Google Scholar]
  10. B. Boutin, C. Chalons and P.A. Raviart, Existence result for the coupling problem of two scalar conservation laws with Riemann initial data. Math. Models Methods Appl. Sci. 20 (2010) 1859–1898. [CrossRef] [Google Scholar]
  11. R. Cautrés, R. Herbin and F. Hubert, The Lions domain decomposition algorithm on non matching cell-centred finite volume meshes. IMA J. Numer. Anal. 24 (2004) 465–490. [CrossRef] [MathSciNet] [Google Scholar]
  12. C. Chainais-Hillairet and J. Droniou, Finite volume schemes for non-coercive elliptic problems with Neumann boundary conditions. IMA J. Numer. Anal. 31 (2011) 61–85. [CrossRef] [MathSciNet] [Google Scholar]
  13. Y. Coudière, J.-P. Vila and P. Villedieu, Convergence rate of a finite volume scheme for a two-dimensional convection-diffusion problem. ESAIM: M2AN 33 (1999) 493–516. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. Y. Coudière, T. Gallouët and R. Herbin, Discrete Sobolev Inequalities and Lp error estimates for finite volume solutions of convection diffusion equations. ESAIM: M2AN 35 (2001) 767–778. [CrossRef] [EDP Sciences] [Google Scholar]
  15. K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. ESAIM: M2AN 39 (2005) 1203–1249. [CrossRef] [EDP Sciences] [Google Scholar]
  16. M. Deininger, J. Jung, R. Skoda, P. Helluy and C.-D. Munz, Evaluation of interface models for 3D-1D coupling of compressible Euler methods for the application on cavitating flows. CEMRACS’11: Multiscale coupling of complex models in scientific computing. ESAIM Proceedings. EDP Sciences Les Ulis 38 (2012) 298–318. [Google Scholar]
  17. 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] [Google Scholar]
  18. 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]
  19. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods. Handb. Numer. Anal. Edited by P.G. Ciarlet and J.L. Lions (2000). [Google Scholar]
  20. F. Filbet, A finite volume scheme for the Patlak-Keller-Segel chemotaxis model. Numer. Math. 104 (2006) 457–488. [CrossRef] [MathSciNet] [Google Scholar]
  21. F. Fontvieille, G.P. Panasenko and J. Pousin, FEM implementation for the asymptotic partial decomposition. Appl. Anal. Int. J. 86 (2007) 519–536. [CrossRef] [MathSciNet] [Google Scholar]
  22. L. Formaggia, F. Nobile, A. Quarteroni and A. Veneziani, Multiscale modelling of the circulatory system: a preliminary analysis. Comput. Visual. Sci. 2 (1999) 75–83. [Google Scholar]
  23. L. Formaggia, J.F. Gerbeau, F. Nobile and A. Quarteroni, On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191 (2001) 561–582. [CrossRef] [MathSciNet] [Google Scholar]
  24. L. Formaggia, A. Quarteroni and A. Veneziani, Cardiovascular Mathematics, Series: Model. Simul. Appl., vol. 1. Springer (2009). [Google Scholar]
  25. T. Gallouët, R. Herbin and M.H. Vignal, Error estimates on the approximate finite volume solution of convection diffusion equations with general boundary conditions. SIAM J. Numer. Anal. 37 (2000) 1935–1972. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Glitzky and J.A. Griepentrog, Discrete Sobolev–Poincaré Inequalities for Voronoi Finite Volume Approximations. SIAM J. Numer. Anal. 48 (2010) 372–391. [Google Scholar]
  27. P. Grisvard, Elliptic Problems in Non Smooth Domains. Pitman (1985). [Google Scholar]
  28. J.M. Hérard and O. Hurisse, Coupling two and one-dimensional unsteady Euler equations through a thin interface. Comput. Fluids 36 (2007) 651–666. [Google Scholar]
  29. R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Method Partial Differ. Eq. 11 (1995) 165–173. [Google Scholar]
  30. J. Heywood, R. Rannacher and S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier–Stokes equations. Int. J. Num. Meth. Fl. 22 (1996) 325–352. [Google Scholar]
  31. A.H. Le and P. Omnes, Discrete Poincaré inequalities for arbitrary meshes in the discrete duality finite volume context. Electronic Trans. Numer. Anal. 40 (2013) 94–119. [Google Scholar]
  32. J.S. Leiva, P.J. Blanco and G.S. Buscaglia, Iterative strong coupling of dimensionally heterogeneous models. Int. J. Numer. Methods Eng. 81 (2010) 1558–1580. [Google Scholar]
  33. J.S. Leiva, P.J. Blanco and G.S. Buscaglia, Partitioned analysis for dimensionally-heterogeneous hydraulic networks. SIAM Multiscale Model. Simul. 9 (2011) 872–903. [Google Scholar]
  34. A.C.I. Malossi, P.J. Blanco, P. Crosetto, S. Deparis and A. Quarteroni, Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels. Multiscale Model. Simul. 11 (2013) 474–506. [Google Scholar]
  35. G.P. Panasenko, Method of asymptotic partial decomposition of domain. Math. Models Methods Appl. Sci. 8 (1998) 139–156. [CrossRef] [Google Scholar]
  36. G.P. Panasenko and M.-C. Viallon, Error estimate in a finite volume approximation of the partial asymptotic domain decomposition. Math. Meth. Appl. Sci. 36 (2013) 1892–1917. [CrossRef] [Google Scholar]
  37. G.P. Panasenko and M.-C. Viallon, The finite volume implementation of the partial asymptotic domain decomposition. Appl. Anal. Int. J. 87 (2008) 1397–1424. [CrossRef] [Google Scholar]
  38. T. Passerini, M. de Luca, L. Formaggia and A. Quarteroni, A 3D/1D geometrical multiscale model of cerebral vasculature. J. Eng. Math. 64 (2009) 319–330. [CrossRef] [Google Scholar]
  39. A. Quarteroni and L. Formaggia, Mathematical Modelling and Numerical Simulation of the Cardiovascular System. Modelling of Living Systems. Edited by N. Ayache. Handb. Numer. Anal. Series (2002). [Google Scholar]
  40. L. Saas, I. Faille, F. Nataf and F. Willien, Finite volume methods for domain decomposition on non matching grids with arbitrary interface conditions. SIAM J. Numer. Anal. 43 (2005) 860–890. [CrossRef] [Google Scholar]
  41. S.A. Urquiza, P.J. Blanco, M.J. Vénere and R.A. Feijóo, Multidimensional modelling for the carotid artery blood flow. Comput. Methods Appl. Mech. Eng. 195 (2006) 4002–4017. [CrossRef] [Google Scholar]
  42. M.-C. Viallon, Error estimate for a 1D-2D finite volume scheme. Comparison with a standard scheme on a 2D non-admissible mesh. C. R. Acad. Sci. Paris, Ser. I 351 (2013) 47–51. [CrossRef] [Google Scholar]
  43. M. Vohralik, On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the sobolev space H1. Numer. Funct. Anal. Optim. 26 (2005) 925–952. [Google Scholar]
  44. M. Vohralik, Numerical methods for nonlinear elliptic and parabolic equations. Application to flow problems in porous and fractured media. Ph.D. thesis, Université de Paris-Sud and Czech Technical University in Prague. [Google Scholar]
  45. S.M. Watanabe, P.J. Blanco and R.A. Feijóo, Mathematical model of blood flow in an anatomically detailed arterial network of the arm. ESAIM: M2AN 47 (2013) 961–985. [CrossRef] [EDP Sciences] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you