Finite element approximation of a nonlinear elliptic equation arising from bimaterial problems in elastic-plastic mechanics

Numerische Mathematik

Volumn 86, Issue 3, 2000, Pages 491-506

  Liu, Wenbin ^a  

^a UNIVERSITY OF KENT   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034397019     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110000157     Document Type: Article

References (16)

1. Barrett, J.W., Elliott, C.M. ( 1987): Fitted and unfitted finite element methods for elliptic equations with smooth interfaces. IMA J.Nurm. Anal. 7, 283-300
2. Barrett, W.J., Liu, W.B. (1993): Finite element approximation of p-Laplacian. Math.Comp. 61,223-239
3. Barrett, W.J., Liu. W.B. (1994): Quasi-norm error bounds for the finite element approximation of a quasi- Newtonian flow. Numer.Math. 68, 437-456
4. Babuska, I. ( 1970): The finite element method for elliptic equations with discontinuous coefficients. Computing 5, 207-213
5. Chow, S.S. (1988): Finite element error estimates for non-linear elliptic equations of monotone type. Numer Math. 54, 373-393
6. Ciarlet, P.G. (1978): The Finite Element Methods for Elliptic Problems. North Holland, Amsterdam
7. Feistauer, M., Sobotikova, V. ( 1990): Finite element approximation of non-linear elliptic problems with discontinuous coefficients. R.A.I.R.O. Analyse Numerique 24,457-500
8. Glowinski, R., Marrocco, A. (1975): Sur l'approximation par element finis d'order un, et la resolution, par penalisation-dualite, d'une classe de problems de Dirichlet non lineaires. R.A.I.R.O.Analyse Numerique 2, 41-64
9. Iwaniec, T., Manfredi, J. (1989): Regularity of p-Harmonic functions on the plane. Rev.Math.Iberoamericana 5, 1-19
10. Liu, W., Barrett, W.J. (1996): Finite element approximation of some degenerate monotone quasilinear elliptic systems. SIAM.J.Numer.Anal. 33, 88-106
11. Liu, W., Barrett, W.J. (1993): A further remark on the regularity of the solutions of p-Laplacian and its applications to their finite element approximation. J.Nonlinear.Anal. 21, 379-387
12. Liu, W., Barrett, W.J. (1993): Higher order regularity for the solutions of some nonlinear degenerate elliptic equations. SIAM.J.Math.Anal. 24, 1522-1536
13. Liu, W. (1999): Elliptic equations arising from bimaterial problems in elastic-plastic mechincan. J. Nonlinear. Anal. 35, 517-529
14. Rice, J.R., Rosengren, G.F. (1968): Plane strain deformation near a crack tip in a power law hardening material. J.Mech.Phys.Solids. 16, 1-12
15. Rice, J.R. (1968): Mathematical analysis in the mechanics of fracture. Fracture-an Advanced Treatise Vol.II. Liebowitz,H (ed). pp. 191-308, New York: Academic
16. Zenisek, A. (1990):The finite element method for nonlinear elliptic equations with discontinuous coefficients. Numer.Math. 58, 51-77