Treatment of material discontinuities in finite element computations. (English) Zbl 0602.73065

We consider finite element analysis of problems with discontinuous material coefficients. For applications in which the material interface crosses an element, we develop special elements with an embedded flux constraint at the interface. This new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by G. P. Steven [ibid. 18, 569-582 (1982; Zbl 0482.76016)]. Supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined. Some local superconvergence behaviour is observed.


74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)


Zbl 0482.76016
Full Text: DOI


[1] Steven, Int. j. numer. methods eng. 18 pp 569– (1982)
[2] Alexander, Accademia Nazionale Dei Lincei, Serie VIII LXVII pp 57– (1979)
[3] Lynch, Int. j. numer. methods eng. 17 pp 81– (1983)
[4] Miller, S I A M J. Numer. Anal. 18 pp 1033– (1981)
[5] Mueller, Int. j. numer. methods eng. 21 pp 2099– (1985)
[6] and , ’An adaptive time discretization procedure for parabolic problems’, in R. Vichnevetsky and R. S. Stepelman (eds), Advances in Computer Methods for Partial Differential Equations-IV, IMACS Proceedings, 1984.
[7] ’Mesh refinement and redistribution’, in Finite Elements for Coupled and Nonlinear Problems, (ed.), Wiley, Chichester (in press).
[8] Wellford, Int. j. numer. methods eng. 11 pp 933– (1977)
[9] Panda, Int. j. numer. methods eng. 14 pp 69– (1979)
[10] Wheeler, S I A M J. Numer. Anal. 11 pp 764– (1974)
[11] Carey, J. Comp. Meth. Appl. Mech. Eng. 35 pp 1– (1982)
[12] Carey, J. Comp. Meth. Appl. Mech. Eng. 50 pp 107– (1985)
[13] Babuška, Computing 5 pp 207– (1970)
[14] and , Finite Elements: Computational Aspects, Prentice-Hall, Englewood Cliffs, NJ, 1984. · Zbl 0558.73064
[15] ’A finite element thermo-structural model for underground coal conversion’, Ph.D. Dissertation, The University of Texas at Austin, (in progress).
[16] and , ’Analysis of material interface discontinuities in finite difference theory’, J. Comp. Physics, (submitted).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.