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An Analysis of a Cell-Vertex Finite Volume Method for a Parabolic Convection-Diffusion Problem
Author(s):
Wen
Guo;
Martin
Stynes.
Journal:
Math. Comp.
66
(1997),
105-124.
MSC (1991):
Primary 65M60, 65M12;
Secondary 76M25
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Abstract:
We examine a cell-vertex finite volume method which is applied to a model parabolic convection-diffusion problem. By using techniques from finite element analysis, local errors away from all layers are obtained in a seminorm that is related to, but weaker than, the norm.
References:
- 1.
- I. Babu\v{s}ka and J. Osborn, Analysis of finite element methods for second order boundary value problems using mesh dependent norms, Numer. Math. 34 (1980), 41 - 62. MR 81g:65143
- 2.
- H. Baumert, P. Braun, E. Glos, W. Müller and G. Stoyan, Modelling and computation of water quality problems in river networks, Lecture Notes in Control and Information Sciences, vol. 23, Springer, Berlin, 1981, pp. 482 - 491.
- 3.
- W. Eckhaus and E. M. de Jager, Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rational Mech. Anal. 23 (1966), 26 - 86. MR 34:6283
- 4.
- R. E. Ewing, The mathematics of reservoir simulation, SIAM, Philadelphia, 1983. MR 85g:76027
- 5.
- S.-Y. Hahn, An upwind' finite element method for electromagnetic field problems in moving media, Intern. J. Numer. Methods Engrg. 24 (1987), 2071 - 2086.
- 6.
- M. Jakob, Heat transfer, Wiley, New York, 1959.
- 7.
- O. A. Lady\v{z}enskaja, V. A. Solonnikov and N. N. Ural
ceva, Linear and quasi-linear equations of parabolic type, Translations of Mathematical Monographs, Vol. 23, American Math. Soc., Providence, R.I., 1968. MR 39:3159b - 8.
- J. A. Mackenzie and K. W. Morton, Finite volume solutions for convection-diffusion test problems, Math. Comp. 60 (1993), 189 - 220. MR 93d:76065
- 9.
- K. W. Morton and M. Stynes, An analysis of the cell vertex method, Math. Modél. Anal. Numér. 28 (1994), 699 - 724. MR 95h:65072
- 10.
- K. W. Morton and E. Süli, Finite volume methods and their analysis, IMA J. Numer. Anal. 11 (1991), 241 - 260. MR 93e:65145
- 11.
- A. H. Nayfeh, Perturbation methods, Wiley, New York, 1973. MR 53:8588
- 12.
- R. E. O'Malley, Singular perturbation methods for ordinary differential equations, Springer-Verlag, New York, 1991. MR 92i:34071
- 13.
- D. W. Peaceman and H. H. Rachford, Numerical calculation of multi-dimensional miscible displacement, Soc. Petroleum Engrg. J. 24 (1962), 327 - 338.
- 14.
- H. S. Price and R. S. Varga, Error bounds for semidiscrete Galerkin approximations of parabolic problems with applications to petroleum reservoir mechanics, in Numerical Solution of Field Problems in Continuum Physics, SIAM-AMS Proc., Vol. 2, 1970, pp. 74 - 94. MR 42:1358
- 15.
- E. Süli, The accuracy of finite volume methods on distorted partitions, in The Mathematics of Finite Elements and Applications (J. R. Whiteman, ed.), VII MAFELAP 1990, Academic Press, New York, 1991, pp. 253 - 260. MR 92i:65171
- 16.
- -, The accuracy of cell vertex finite volume methods on quadrilateral meshes, Math. Comp. 59 (1992), 359 - 382. MR 93a:65158
- 17.
- M. Van Dyke, Perturbation methods in fluid mechanics, Parabolic Press, Stanford, CA, 1975. MR 54:4315
- 18.
- M. I. Vishik and L. A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with a small parameter, Uspekhi Mat. Nauk. 12 (1957), 3 - 122 = Amer. Math. Soc. Transl., Ser. 2, 20 (1962), pp. 239 - 364. MR 25:322
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Additional Information:
Wen
Guo
Affiliation:
Department of Mathematics, University College, Cork, Ireland
Martin
Stynes
Affiliation:
Department of Mathematics, University College, Cork, Ireland
Email:
stynes@ucc.ie
DOI:
10.1090/S0025-5718-97-00795-3
PII:
S 0025-5718(97)00795-3
Received by editor(s):
August 23, 1993
Received by editor(s) in revised form:
February 22, 1995 and January 26, 1996
Copyright of article:
Copyright
1997,
American Mathematical Society
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