An analysis of the cell vertex method

K. W. Morton; M. Stynes

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 6, page 699-724
  • ISSN: 0764-583X

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Morton, K. W., and Stynes, M.. "An analysis of the cell vertex method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.6 (1994): 699-724. <http://eudml.org/doc/193756>.

@article{Morton1994,
author = {Morton, K. W., Stynes, M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {cell vertex method; nonconforming Petrov-Galerkin method; finite element methods; finite volume methods; convection-diffusion problem; error estimates},
language = {eng},
number = {6},
pages = {699-724},
publisher = {Dunod},
title = {An analysis of the cell vertex method},
url = {http://eudml.org/doc/193756},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Morton, K. W.
AU - Stynes, M.
TI - An analysis of the cell vertex method
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 6
SP - 699
EP - 724
LA - eng
KW - cell vertex method; nonconforming Petrov-Galerkin method; finite element methods; finite volume methods; convection-diffusion problem; error estimates
UR - http://eudml.org/doc/193756
ER -

References

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  1. [1] J. W. BARRETT and K. W. MORTON, 1984, Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems, Computer Methods in Applied Mechanics and Engineering, 45, 97-122. Zbl0562.76086MR759805
  2. [2] P. W. HEMKER, 1977, A numerical study of stiff two-point boundary problems, PhD thesis, Mathematisch Centrum, Amsterdam. Zbl0426.65043MR488784
  3. [3] R. B. KELLOGG and A. TSAN, 1978, Analysis of some difference approximations for a singular perturbation problem without turning points, Mathematics of Computation, 32, 1025-1039. Zbl0418.65040MR483484
  4. [4] J. A. MACKENZIE, 1991, Cell vertex finite volume methods for the solution of the compressible Navier-Stokes equations, PhD thesis, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD. 
  5. [5] J. A. MACKENZIE and K. W. MORTON, 1992Finite volume solutions of convection-diffusion test problems, Mathematics of Computation, 60(201), 189-220. Zbl0797.76072MR1153168
  6. [6] K. W. MORTON, 1991, Finite volume methods and their analysis, in J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications VII MAFELAP 1990, Academic Press, 189-214. Zbl0843.65070MR1132499
  7. [7] K. W. MORTON, 1992, Upwinded test functions for finite element and finite volume methods, in D. F. Griffiths and G. A. Watson, editors, Numerical analysis 1991 Proceedings of the 14th Dundee Conference, June 1991, number 260 in Pitman Research Notes in Mathematics Series, pp. 128-141, Longman Scientific and Technical. Zbl0801.65096MR1177232
  8. [8] K. W. MORTON, P. I. CRUMPTON and J. A. MACKENZIE, 1993, Cell vertex methods for inviscid and viscous flows, Computers Fluids, 22(2/3), 91-102. Zbl0779.76073
  9. [9] K. W. MORTON and E. SÜLI, 1991, Finite volume methods and their analysis, IMA Journal of Numerical Analysis, 11, 241-260. Zbl0729.65087MR1105229
  10. [10] M. STYNES and E. O'RIORDAN, 1991, An analysis of a singularly perturbed two-point boundary value problem using only finite element techniques, Mathematics of Computation, 56, 663-676. Zbl0718.65062MR1068809
  11. [11] E. SÜLI, 1991, The accuracy of finite volume methods on distorted partitions. In J. R. Whiteman, editor. The Proceedings of the Conference on The Mathematics of Finite Elements and Applications VII MAFELAP, pp. 253-260. Academic Press. MR1132503
  12. [12] E. SÜLI, 1992, The accuracy of cell vertex finite volume methods on quadrilateral meshes, Mathematics of Computation, 59(200), 359-382. Zbl0767.65072MR1134740

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