Free Access
Issue
ESAIM: M2AN
Volume 35, Number 2, March/April 2001
Page(s) 355 - 387
DOI https://doi.org/10.1051/m2an:2001119
Published online 15 April 2002
  1. L. Angermann, An introduction to finite volume methods for linear elliptic equations of second order. Preprint 164, Institut für Angewandte Mathematik, Universität Erlangen (1995). [Google Scholar]
  2. Lutz Angermann, A finite element method for the numerical solution of convection-dominated anisotropic diffusion equations. Numer. Math. 85 (2000) 175-195. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Angot, V. DolejšÍ, M. Feistauer and J. Felcman, Analysis of a combined barycentric finite volume - finite element method for nonlinear convection diffusion problems. Appl. Math., Praha 43 (1998) 263-311. [Google Scholar]
  4. I. Babuska and W.C. Rheinboldt, Error estimators for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978) 736-754. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Bänsch, Local mesh refinement in 2 and 3 dimensions. IMPACT Comput. Sci. Engrg. 3 (1991) 181-191. [CrossRef] [MathSciNet] [Google Scholar]
  6. R. Becker and R. Rannacher, A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math. 4 (1996) 237-264. [MathSciNet] [Google Scholar]
  7. F. Bouchut and B. Perthame, Kruzkov's estimates for scalar conservation laws revisited. Trans. Amer. Math. Soc. 350 (1998) 2847-2870. [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Carrillo, Entropy solutions for nonlinear degenerate problems. Arch. Ration. Mech. Anal. 147 (1999) 269-361. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Chainais-Hillairet, Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimates. ESAIM: M2AN 33 (1999) 129-156. [CrossRef] [EDP Sciences] [Google Scholar]
  10. S. Champier, Error estimates for the approximate solution of a nonlinear hyperbolic equation with source term given by finite volume scheme. Preprint, UMR 5585, Saint-Etienne University (1998). [Google Scholar]
  11. G. Chavent and J. Jaffre, Mathematical models and finite elements for reservoir simulation. Elsevier, New York (1986). [Google Scholar]
  12. B. Cockburn, F. Coquel and P.G. Lefloch, An error estimate for finite volume methods for multidimensional conservation laws. Math. Comput. 63 (1994) 77-103. [CrossRef] [Google Scholar]
  13. B. Cockburn and H. Gau, A posteriori error estimates for general numerical methods for scalar conservation laws. Comput. Appl. Math. 14 (1995) 37-47. [Google Scholar]
  14. B. Cockburn and P.A. Gremaud, A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach. Math. Comput. 65 (1996) 533-573. [CrossRef] [MathSciNet] [Google Scholar]
  15. B. Cockburn and G. Gripenberg, Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations. J. Differential Equations 151 (1999) 231-251. [CrossRef] [MathSciNet] [Google Scholar]
  16. W. Dörfler, Uniformly convergent finite-element methods for singularly perturbed convection-diffusion equations. Habilitationsschrift, Mathematische Fakultät, Freiburg (1998). [Google Scholar]
  17. K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems. Math. Comput. 60 (1993) 167-188. [CrossRef] [Google Scholar]
  18. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. II: Optimal error estimates in LL2 and LL. SIAM J. Numer. Anal. 32 (1995) 706-740. [CrossRef] [MathSciNet] [Google Scholar]
  19. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. IV: Nonlinear Problems. SIAM J. Numer. Anal. 32 (1995) 1729-1749. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Evje, K.H. Karlsen and N.H. Risebro, A continuous dependence result for nonlinear degenerate parabolic equations with spatial dependent flux function. Preprint, Department of Mathematics, Bergen University (2000). [Google Scholar]
  21. R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, Error estimates for the approximate solution of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18 (1998) 563-594. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Eymard, T. Gallouët, R. Herbin and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations. Preprint LATP 00-20, CMI, Provence University, Marseille (2000). [Google Scholar]
  23. P. Frolkovic, Maximum principle and local mass balance for numerical solutions of transport equations coupled with variable density flow. Acta Math. Univ. Comenian. 67 (1998) 137-157. [MathSciNet] [Google Scholar]
  24. J. Fuhrmann and H. Langmach, Stability and existence of solutions of time-implicit finite volume schemes for viscous nonlinear conservation laws. Preprint 437, Weierstraß-Institut, Berlin (1998). [Google Scholar]
  25. R. Helmig, Multiphase flow and transport processes in the subsurface: A contribution to the modeling of hydrosystems. Springer, Berlin, Heidelberg (1997). [Google Scholar]
  26. R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Methods Partial Differential Equation 11 (1995) 165-173. [CrossRef] [MathSciNet] [Google Scholar]
  27. P. Houston and E. Süli, Adaptive lagrange-galerkin methods for unsteady convection-dominated diffusion problems. Report 95/24, Numerical Analysis Group, Oxford University Computing Laboratory (1995). [Google Scholar]
  28. J. Jaffre, Décentrage et élements finis mixtes pour les équations de diffusion-convection. Calcolo 21 (1984) 171-197. [CrossRef] [MathSciNet] [Google Scholar]
  29. V. John, J.M. Maubach and L. Tobiska, Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems. Numer. Math. 78 (1997) 165-188. [CrossRef] [MathSciNet] [Google Scholar]
  30. C. Johnson, Finite element methods for convection-diffusion problems, in Proc. 5th Int. Symp. (Versailles, 1981), Computing methods in applied sciences and engineering V (1982) 311-323. [Google Scholar]
  31. K.H. Karlsen and N.H. Risebro, On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Preprint 143, Department of Mathematics, Bergen University (2000). [Google Scholar]
  32. D. Kröner, Numerical schemes for conservation laws. Teubner, Stuttgart (1997). [Google Scholar]
  33. D. Kröner and M. Ohlberger, A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions. Math. Comput. 69 (2000) 25-39. [Google Scholar]
  34. D. Kröner and M. Rokyta, A priori error estimates for upwind finite volume schemes in several space dimensions. Preprint 37, Math. Fakultät, Freiburg (1996). [Google Scholar]
  35. S.N. Kruzkov, First order quasilinear equations in several independent variables. Math. USSR Sbornik 10 (1970) 217-243. [CrossRef] [Google Scholar]
  36. 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) 159-193. [Google Scholar]
  37. J. Málek, J. Nečas, M. Rokyta and M. Růžička, Weak and measure-valued solutions to evolutionary PDEs, in Applied Mathematics and Mathematical Computation 13, Chapman and Hall, London, Weinheim, New York, Tokyo, Melbourne, Madras (1968). [Google Scholar]
  38. M. Marion and A. Mollard, An adaptive multi-level method for convection diffusion problems. ESAIM: M2AN 34 (2000) 439-458. [CrossRef] [EDP Sciences] [Google Scholar]
  39. R.H. Nochetto, A. Schmidt and C. Verdi, A posteriori error estimation and adaptivity for degenerate parabolic problems. Math. Comput. 69 (2000) 1-24. [Google Scholar]
  40. M. Ohlberger, Convergence of a mixed finite element-finite volume method for the two phase flow in porous media. East-West J. Numer. Math. 5 (1997) 183-210. [MathSciNet] [Google Scholar]
  41. M. Ohlberger, A posteriori error estimates for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations. Numer. Math. 87 (2001) 737-761. [CrossRef] [MathSciNet] [Google Scholar]
  42. Ch. Rohde, Entropy solutions for weakly coupled hyperbolic systems in several space dimensions. Z. Angew. Math. Phys. 49 (1998) 470-499. [CrossRef] [MathSciNet] [Google Scholar]
  43. Ch. Rohde, Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D. Numer. Math. 81 (1998) 85-123. [CrossRef] [MathSciNet] [Google Scholar]
  44. H.-G. Roos, M. Stynes and L. Tobiska, Numerical methods for singularly perturbed differential equations. Convection-diffusion and flow problems, in Springer Ser. Comput. Math. 24, Springer-Verlag, Berlin (1996). [Google Scholar]
  45. E. Tadmor, Local error estimates for discontinuous solutions of nonlinear hyperbolic equations. SIAM J. Numer. Anal. 28 (1991) 891-906. [NASA ADS] [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  46. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques, in Wiley-Teubner Ser. Adv. Numer. Math., Teubner, Stuttgart (1996). [Google Scholar]
  47. R. Verfürth, A posteriori error estimators for convection-diffusion equations. Numer. Math. 80 (1998) 641-663. [CrossRef] [MathSciNet] [Google Scholar]
  48. J.P. Vila, Convergence and error estimates in finite volume schemes for general multi-dimensional scalar conservation laws. I Explicit monotone schemes. ESAIM: M2AN 28 (1994) 267-295. [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