EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 51 / No 3 (May-June 2017) ESAIM: M2AN, 51 3 (2017) 919-947 References
Free Access
Issue
ESAIM: M2AN
Volume 51, Number 3, May-June 2017
Page(s) 919 - 947
DOI https://doi.org/10.1051/m2an/2016042
Published online 14 April 2017
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York e.a. (1975). [Google Scholar]
  2. P. Angot, V. Dolejší, M. Feistauer and J. Felcman, Analysis of a combined barycentric finite volume – nonconforming finite element method for nonlinear convection-diffusion problems. Appl. Math. 43 (1998) 263–310. [Google Scholar]
  3. B. Ayuso and L.D. Marini, Discontinuous Galerkin methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 47 (2009) 1391–1420. [Google Scholar]
  4. G.R. Barrenechea, V. John and P. Knobloch, A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equation. Math. Model. Numer. Anal. 47 (2013) 1335–1366. [CrossRef] [Google Scholar]
  5. M. Bejček, M. Feistauer, T. Gallouët, J. Hájek and R. Herbin, Combined triangular FV-triangular FE method for nonlinear convection-diffusion problems. Z. Angew. Math. Mech. 87 (2007) 499–517. [Google Scholar]
  6. S.C. Brenner, The Mathematical Theory of Finite Element Methods (2nd ed.). Springer, New York e.a. (2002). [Google Scholar]
  7. S.C. Brenner, Poincaré-Friedrichs inequalities for piecewise -functions. SIAM J. Numer. Anal. 41 (2003) 306–324. [Google Scholar]
  8. A. Buffa, T.J.R. Hughes and G. Sangalli, Analysis of multiscale discontinuous Galerkin method for convection-diffusion problems. SIAM J. Numer. Anal. 44 (2006) 1420–1440. [Google Scholar]
  9. E. Burman and M. A. Fernández, Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation. Comput. Methods Appl. Mech. Engrg. 198 (2009) 2508–2519. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Causin, R. Sacco and C.L. Bottasso, Flux-upwind stabilization of the discontinuous Petrov-Galerkin formulation with Lagrangian multipliers for advection-diffusion problems. ESAIM: M2AN 39 (2005) 1087–1114. [CrossRef] [EDP Sciences] [Google Scholar]
  11. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1979). [Google Scholar]
  12. P. Deuring, A finite element – finite volume discretization of convection-reaction-diffusion equations with mixed nonhomogeneous boundary conditions: error estimates. To appear in Numer. Methods Partial Differ. Equ. [Google Scholar]
  13. P. Deuring and M. Mildner, Error estimates for a finite element – finite volume discretization of convection-diffusion equations. Appl. Numer. Math. 61 (2011) 785–801. [Google Scholar]
  14. P. Deuring and M. Mildner, Stability of a combined finite element – finite volume discretization of convection-diffusion equations. Numer. Methods Partial Differ. Equ. 28 (2012) 402–424. [Google Scholar]
  15. P. Deuring, R. Eymard and M. Mildner, L-stability independent of diffusion for a finite element – finite volume discretization of a linear convection-diffusion equation. SIAM J. Numer. Anal. 53 (2015) 508–526. [Google Scholar]
  16. A. Devinatz, R. Ellis and A. Friedman, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivative. II. Indiana Univ. Math. J. 23 (1973) 991–1011. [CrossRef] [MathSciNet] [Google Scholar]
  17. V. Dolejší, M. Feistauer and J. Felcman, On the discrete Friedrichs inequality for non-conforming finite elements. Numer. Funct. Anal. Optim. 20 (1999) 437–447. [Google Scholar]
  18. V. Dolejší, M. Feistauer, J. Felcman and A. Kliková, Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems. Appl. Math. 47 (2002) 301–340. [Google Scholar]
  19. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Appl. Math. Sci. 159, Springer, New York e.a. (2004). [Google Scholar]
  20. R. Eymard, T. Gallouët, R. Herbin and J.-C. Latché, A convergent finite element - finite volume scheme for the compressible Stokes problem. Part II: the isentropic case. Math. Comput. 270 649–675 (2010). [Google Scholar]
  21. R. Eymard, D. Hilhorst and M. Vohralik, A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Numer. Math. 105 (2006) 73–131. [Google Scholar]
  22. R. Eymard, D. Hilhorst and M. Vohralik, A combined finite volume – finite element scheme for the discretization of strongly nonlinear convection-diffusion-reaction problems on nonmatching grids. Numer. Methods Partial Differ. Equ. 26 (2010) 612–646. [Google Scholar]
  23. M. Feistauer, Mathematical Methods in Fluid Dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics 67. Longman, Harlow (1993). [Google Scholar]
  24. M. Feistauer, J. Felcman and M. Lukáčová-Medvid’ová, On the convergence of a combined finite volume – finite element method for nonlinear convection-diffusion problems. Numer. Methods Partial Differ. Equ. 13 (1997) 163–190. [Google Scholar]
  25. M. Feistauer, J. Felcman, M. Lukáčová-Medvid’ová and G. Warnecke, Error estimates for a combined finite volume – finite element method for nonlinear convection-diffusion problems. SIAM J. Math. Anal. 36 (1999) 1528–1548. [Google Scholar]
  26. M. Feistauer, J. Felcman and I. Straškraba, Mathematical and Computational Methods for Compressible Flow. Clarendon Press, Oxford (2003). [Google Scholar]
  27. M. Feistauer, V. Kučera, K. Najzan and J. Prokopová, Analysis of a space-time discontinuous Galerkin method for nonlinear convection-diffusion problems. Numer. Math. 117 (2011) 251–288. [Google Scholar]
  28. M. Feistauer, J. Slavík and P. Stupka, On the convergence of a combined finite volume – finite element method for nonlinear convection-diffusion problems. Explicit schemes. Numer. Methods Partial Differ. Equ. 15 (1999) 215–235. [Google Scholar]
  29. S. Fučík, O. John and A. Kufner, Function Spaces. Noordhoff, Leyden (1977). [Google Scholar]
  30. T. Gallouët, R. Herbin and J.-C. Latché, A convergent finite element – finite volume scheme for the compressible Stokes problem. Part I: the isothermal case. Math. Comput. 267 (2009) 1333–1352. [Google Scholar]
  31. V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations. Springer, Berlin e.a. (1986). [Google Scholar]
  32. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, London (1985). [Google Scholar]
  33. L. Hallo, C. Le Ribault and M. Buffat, An implicit mixed finite-volume-finite-element method for solving 3D turbulent compressible flows. Int. J. Numer. Meth. Fluids 25 (1997) 1241–1261. [CrossRef] [Google Scholar]
  34. P.-Wen Hsieh and S.-Y. Yang, On efficient least-squares finite element methods for convection-dominated problems. Comput. Methods Appl. Mech. Engrg. 199 (2009) 183–196. [CrossRef] [MathSciNet] [Google Scholar]
  35. A. Jonsson and H. Wallin, Function Spaces on Subsets of . Harwood Academic Publishers, New York (1984). [Google Scholar]
  36. N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988). [Google Scholar]
  37. P. Knobloch, Uniform validity of discrete Friedrich’s inequality for general nonconforming finite element spaces. Numer. Funct. Anal. Optimiz. 22 (2001) 107–126. [CrossRef] [Google Scholar]
  38. R.C. Leal Toledo and V. Ruas, Numerical analysis of a least-squares finite element method for the time-dependent advection-diffusion equation. J. Comp. Appl. Math. 235 (2011) 3615–3631. [CrossRef] [Google Scholar]
  39. Z. Li, Convergence analysis of an upwind mixed element method for advection diffusion problems. Appl. Math. Comput. 212 (2009) 318–326. [MathSciNet] [Google Scholar]
  40. A.S. Mounim, A stabilized finite element method for convection-diffusion problems. Numer. Methods Partial Differ. Equ. 28 (2012) 1916–1943. [Google Scholar]
  41. K. Ohmori and T. Ushijima, A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations. RAIRO Modél. Math. Anal. Numér. 18 (1984) 309–332. [CrossRef] [Google Scholar]
  42. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer Series in Computational Mathematics 23. Springer, Berlin e.a. (1994). [Google Scholar]
  43. Y. Ren, A. Cheng and H. Wang, A uniformly optimal-order estimate for finite volume method for advection-diffusion equation. Numer. Methods Partial Differ. Equ. 30 (2014) 17–43. [Google Scholar]
  44. H.-G. Roos, M. Stynes and L. Tobiska, Robust Numerical Methods for Singularly Perturbed Differential Equations (2nd ed.). Springer Series in Computational Mathematics 24. Springer, New York e.a. (2008). [Google Scholar]
  45. H.L. Royden, Real Analysis. Macmillan, New York (1968). [Google Scholar]
  46. R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977). [Google Scholar]
  47. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North Holland, Amsterdam e.a. (1978). [Google Scholar]
  48. R.Verfürth, Robust a posteriori error estimates for steady convection-diffusion equations. SIAM J. Numer. Anal. 43 (2005) 1766–1782. [Google Scholar]
  49. R.Verfürth, Robust a posteriori error estimates for unsteady convection-diffusion equations. SIAM J. Numer. Anal. 43 (2005) 1783–1802. [Google Scholar]
  50. M. Vlasák, V. Dolejší and J. Hájek, A priori error estimates of an extrapolated space-time discontinuous Galerkin method for nonlinear convection-diffusion problems. Numer. Methods Partial Differ. Equ. 27 (2011) 1456–1482. [Google Scholar]
  51. M. Vohralík, On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space . Numer. Funct. Anal. Optimiz. 26 (2005) 925–952. [CrossRef] [MathSciNet] [Google Scholar]
  52. J. Wloka, Partial Differential Equations. Cambridge University Press, Cambridge e.a. (1987). [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