A convergence analysis of an h-version finite-element method with high-order elements for two-dimensional elasto-plasticity problems

SIAM Journal on Numerical Analysis

Volumn 34, Issue 3, 1997, Pages 998-1036

  Yiwei, L I ^a,b   Babuška, Ivo ^a  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Finite element method; Gauge function method; High order finite element spaces

Indexed keywords

EID: 0345908383     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036142994263578     Document Type: Article

References (20)

1. R. A. ADAMS, Sobolev Spaces, Academic Press, New York, San Diego, CA. 1975.
2. I. BABUŠKA, Y. Li, AND K. L. JERINA, Reliability of computational analysis of plasticity problems, in Nonlinear Computational Mechanics, P. Wriggers, W. Wagner, eds., Springer-Verlag, Berlin, New York, 1991.
3. K. J, BATHE, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1982.
4. E. BONNETIER, Ph.D. thesis, Mathematical Treatment of the Uncertainties Appearing in the Formulation of Some Models of Plasticity, Institute for Physical Science & Technology and Department of Mathematics, The University of Maryland at College Park, 1988.
5. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland Amsterdam, 1978.
6. G. R. COWPER, Gaussian quadrature formulas for triangles, Internat. J. Numer. Methods Engrg., 7 (1973), pp. 405-408.
7. D. A. DUNAVANT, High degree efficient symmetrical Gaussian quadrature rules for the triangle, Internat. J. Numer, Methods Engrg., 21 (1985), pp. 1129-1148.
8. G. DUVAUT AND J. L. LIONS, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, New York, 1976.
9. I. EKELAND AND R. TEMAM, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
10. L. C. EVANS, Lecture Notes on Partial Differential Equations, Department of Mathematics, University of California, Berkeley, CA.
11. G. FICHERA, Existence theorems in elasticity-boundary value problems of elasticity with unilateral constraints, in Encyclopedia of Physics, S. Flügge, Chief Ed., Vol. VIa/2: Mechanics of Solids II, C. Truesdell, ed., Springer-Verlag, Berlin, 1972, pp. 347-424.
12. P. C. HAMMER, O. J. MARLOWE, AND A. H. STROUD, Numerical integration over Simplexes and cones, Math. Tabl. Natn. Res. Coun. Wash., 10, (1956) pp. 130-137.
13. C. JOHNSON, Existence theorems for plasticity problems, J. Math. Pures Appl. (9), 55, (1976), pp. 431-444.
14. C. JOHNSON, On plasticity with hardening, J. Math. Anal. Appl., 62 (1978), pp. 325-336.
15. V. I. KRYLOV, Approximate Calculation of Integrals, Macmillan, New York, 1962.
16. T. MIYOSHI, Foundations of the Numerical Analysis of Plasticity, Lecture Notes Numer. Appl. Anal., 7, North-Holland, Amsterdam, 1985.
17. K. REKTORYS, The Method of Discretization in Time and Partial Differential Equations, D. Reidel, Boston, MA, 1982.
18. H. L. ROYDEN, Real Analysis, 3rd ed., Macmillan, New York, 1988.
19. W. RUDIN, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987.
20. M. ZYCZKOWSKI, Combined Loading in the Theory of Plasticity, P.W.N. Polish Scientific Publishers, Warsaw, 1981.