Free Access
Volume 36, Number 2, March/April 2002
Page(s) 307 - 324
Published online 15 May 2002
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. R.E. Bank and D.J. Rose, Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777-787. [CrossRef] [MathSciNet] [Google Scholar]
  3. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). [Google Scholar]
  4. B. Brighi, M. Chipot and E. Gut, Finite differences on triangular grids. Numer. Methods Partial Differential Equations 14 (1998) 567-579. [CrossRef] [MathSciNet] [Google Scholar]
  5. Z. Cai, On the finite volume element method. Numer. Math. 58 (1991) 713-735. [Google Scholar]
  6. 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]
  7. P. Chatzipantelidis, A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions. Numer. Math. 82 (1999) 409-432. [CrossRef] [MathSciNet] [Google Scholar]
  8. P. Chatzipantelidis, R.D. Lazarov and V. Thomée, Error estimates for the finite volume element method for parabolic pde's in convex polygonal domains. In preparation. [Google Scholar]
  9. P. Chatzipantelidis and R.D. Lazarov, The finite volume element method in nonconvex polygonal domains. To appear in Proceedings of the Third International Symposium on Finite Volumes for Complex Applications, Hermes Science Publications, Paris (2002). [Google Scholar]
  10. P. Chatzipantelidis, Ch. Makridakis and M. Plexousakis, A-posteriori error estimates of a finite volume scheme for the Stokes equations. In preparation. [Google Scholar]
  11. S.H. Chou, Analysis and convergence of a covolume method for the generalized Stokes problem. Math. Comp. 66 (1997) 85-104. [CrossRef] [MathSciNet] [Google Scholar]
  12. S.H. Chou and Q. Li, Error estimates in L2, H1 and L in covolume methods for elliptic and parabolic problems: a unified approach. Math. Comp. 69 (2000) 103-120. [Google Scholar]
  13. P.G. Ciarlet, Basic Error Estimates for Elliptic Problems. Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam (1991) 17-351. [Google Scholar]
  14. M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equation I. RAIRO Anal. Numér. 7 (1973) 33-76. [Google Scholar]
  15. R.E. Ewing, R.D. Lazarov and Y. Lin, Finite Volume Element Approximations of Nonlocal Reactive Flows in Porous Media. Numer. Methods Partial Differential Equations 16 (2000) 285-311. [Google Scholar]
  16. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods. Handbook of Numerical Analysis, Vol. VII, North-Holland, Amsterdam (2000). [Google Scholar]
  17. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Massachusetts (1985). [Google Scholar]
  18. W. Hackbusch, On first and second order box schemes. Comput. 41 (1989) 277-296. [Google Scholar]
  19. H. Jianguo and X. Shitong, On the finite volume element method for general self-adjoint elliptic problems. SIAM J. Numer. Anal. 35 (1998) 1762-1774. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Kang and D.Y. Kwak, Error estimate in L2 of a covolume method for the generalized Stokes Problem. Proceedings of the eight KAIST Math Workshop on Finite Element Method, KAIST (1997) 121-139. [Google Scholar]
  21. G. Kossioris, Ch. Makridakis and P.E. Souganidis, Finite volume schemes for Hamilton-Jacobi equations. Numer. Math. 83 (1999) 427-442. [CrossRef] [MathSciNet] [Google Scholar]
  22. F. Liebau, The finite volume element method with quadratic basis functions. Comput. 57 (1996) 281-299. [CrossRef] [MathSciNet] [Google Scholar]
  23. I.D. Mishev, Finite volume element methods for non-definite problems. Numer. Math. 83 (1999) 161-175. [CrossRef] [MathSciNet] [Google Scholar]
  24. K.W. Morton, Numerical Solution of Convection-Diffusion Problems. Chapman & Hall, London (1996). [Google Scholar]
  25. M. Plexousakis and G.E. Zouraris, High-order locally conservative finite volume-type approximations of one dimensional elliptic problems. Technical Report, TRITA-NA-0138, NADA, Royal Institute of Technology, Sweden. [Google Scholar]
  26. H.-G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations. Springer-Verlag, Berlin (1996). [Google Scholar]
  27. T. Schmidt, Box schemes on quadrilateral meshes. Comput. 51 (1994) 271-292. [Google Scholar]
  28. R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1979). [Google Scholar]
  29. A. Weiser and M.F. Wheeler, On convergence of Block-Centered finite differences for elliptic problems. SIAM J. Num. Anal. 25 (1988) 351-375. [Google Scholar]

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