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Analysis of material interface dicontinuities and superconvergent fluxes in finite difference theory.(English)Zbl 0632.76110

An analysis of material interface discontinuities is developed and applied in finite difference theory to determine mathematically rigorous averaging techniques for material properties. This result is compared with other averaging techniques, particularly harmonic averaging, which is often applied in practice. We also develop a class of formulas of high accuracy for post-processing the difference formula to compute derivatives (fluxes, stresses), and conduct supporting numerical studies.

MSC:

76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
76M99 Basic methods in fluid mechanics

Cite

References:

[1]Aziz, K.; Settari, A., Petroleum Reservoir Simulation, ((1979), Applied Science Publ., Ltd: Applied Science Publ., Ltd London), 83
[2]Babuska, I., Computing, 5, 207 (1970) ·Zbl 0199.50603
[3]Bramble, J. H.; Hubbard, B. E., Contribs. to Diff. Eqs., 3, 399 (1964)
[4]Carey, G. F., J. Comput. Meth. Appl. Mech. Eng., 35, 1 (1982) ·Zbl 0478.73052
[5]Carey, G. F.; Chow, S. S.; Seager, M., J. Comput. Meth. Appl. Mech. Eng., 50, 107 (1985) ·Zbl 0546.73057
[6]Carey, G. F.; Oden, J. T., Finite Elements: Computational Aspects, ((1983), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ), 173 ·Zbl 0496.65055
[7]Carey, G. F.; Oden, J. T., Finite Elements: A Second Course, ((1983), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ), 221 ·Zbl 0515.65075
[8]Dupont, T., SIAM J. Numer. Anal., 13, 362 (1976) ·Zbl 0332.65050
[9]MacKinnon, R. J.; Carey, G. F., Int. J. Numer. Meth. Eng., 24, 393 (1987) ·Zbl 0602.73065
[10]MacKinnon, R. J.; Carey, G. F., Superconvergent Derivatives: A Taylor Series Analysis (1987), (in preparation) ·Zbl 0709.73073
[11]Patankar, S. V., Numerical Heat Transfer and Fluid Flow, ((1980), McGraw-Hill: McGraw-Hill New York), 44 ·Zbl 0595.76001
[12]Tikhonov, A. N.; Samarskii, A. A., USSR Comput. Math. Math. Phys., 1, 5 (1962)
[13]Wheeler, M. F., SIAM J. of Numer. Anal., 11, 764 (1974) ·Zbl 0292.65046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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