Functional a posteriori error estimates for incremental models in elasto-plasticity

Central European Journal of Mathematics

Volumn 7, Issue 3, 2009, Pages 506-519

  Repin, Sergey I ^a   Valdman, Jan ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

A posteriori error estimates; Elasto plastic problem with isotropic hardening; Variational inequalities

Indexed keywords

EID: 69349084843     PISSN: 18951074     EISSN: 16443616     Source Type: Journal    
DOI: 10.2478/s11533-009-0035-2     Document Type: Article

References (37)

1. Ainsworth M., Oden J.T., A posteriori error estimation in finite element analysis, Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs, and Tracts, Wiley and Sons, New York, 2000
2. Alberty J., Carstensen C., Numerical analysis of time-depending primal elastoplasticity with hardening, SIAM J. Numer. Anal., 2000, 37, 1271-1294
3. Alberty J., Carstensen C., Zarrabi D., Adaptive numerical analysis in primal elastoplasticity with hardening, Comput. Methods Appl. Mech. Engrg., 1999, 171, 175-204
4. Babuška I., Strouboulis T., The finite element method and its reliability, Oxford University Press, New York, 2001
5. Bangerth W., Rannacher R., Adaptive finite element methods for differential equations, Birkhäuser, Berlin, 2003
6. 1 regularity, In: Lions J.L. (Ed.) et al., Boundary value problems for partial differential equations and applications, Dedicated to Enrico Magenes on the occasion of his 70th birthday, Paris: Masson. Res. Notes Appl. Math., 1993, 29, 3-25
7. Bildhauer M., Fuchs M., Repin S., A posteriori error estimates for stationary slow flows of power-law fluids, Journal of Non-Newtonian Fluid Mechanics, 2007, 142, 112-122
8. Bildhauer M., Fuchs M., Repin S., A functional type a posteriori error analysis for Ramberg-Osgood Model, ZAMM Z. Angew. Math. Mech., 2007, 87(11-12), 860-876
9. Blaheta R., Numerical methods in elasto-plasticity, Comput. Methods Appl. Mech. Engrg., 1997, 147, 167-185
10. Brokate M., Carstensen C., Valdman J., A quasi-static boundary value problem in multi-surface elastoplasticity, I, Analysis, Math. Methods Appl. Sci., 2004, 27, 1697-1710
11. Brokate M., Carstensen C., Valdman J., A quasi-static boundary value problem in multi-surface elastoplasticity, II, Numerical solution, Math. Methods Appl. Sci., 2005, 28, 881-901
12. Brokate M., Sprekels J., Hysteresis and phase transitions, Springer, New York, 1996
13. Carstensen C., Numerical analysis of the primal problem of elastoplasticity with hardening, Numer. Math., 1999, 82(4), 577-597
14. Carstensen C., Orlando A., Valdman J., A convergent adaptive finite element method for the primal problem of elastoplasticity, Internat. J. Numer. Methods Engrg., 2006, 67(13), 1851-1887
15. Ekeland I., Teman R., Convex analysis and variational problems, North-Holland, Oxford, 1976
16. Fuchs M., Repin S., Estimates for the deviation from the exact solutions of variational problems modeling certain classes of generalized Newtonian fluids, Math. Methods Appl. Sci., 2006, 29, 2225-2244
17. Glowinski R., Lions J.L., Tremolieres R., Analyse numerique des inequations variationnelles, Dunod, Paris, 1976 (in French)
18. Gruber P., Valdman J., Implementation of an elastoplastic solver based on the Moreau, Yosida theorem, Math. Comput. Simulation, 2007, 76(1-3), 73-81
19. Gruber P., Valdman J., Solution of one-time-step problems in elastoplasticity by a slant Newton method, SIAM J. Sci. Comput., 2009, 31(2), 1558-1580
20. Han W., Reddy B.D., Computational plasticity: The variational basis and numerical analysis, Comput. Methods Appl. Mech. Engrg., 1995, 283-400
21. Hofinger A., Valdman J., Numerical solution of the two-yield elastoplastic minimization problem, Computing, 2007, 81, 35-52
22. Krejčí P., Hysteresis, convexity and dissipation in hyperbolic equations, GAKUTO Internat. Ser. Math. Sci. Appl., Vol. 8, Gakkotosho, Tokyo, 1996
23. Lions J.L., Stampacchia G., Variational inequalities, Comm. Pure Appl. Math., 1967, XX(3), 493-519
24. Neittaanmäki P., Repin S., Reliable methods for computer simulation, Error control and a posteriori estimates, Elsevier, New York, 2004
25. Rannacher R., Suttmeier F.T., A posteriori error estimation and mesh adaptation for finite element models in elastoplasticity, Comput. Methods Appl. Mech. Engrg., 1999, 176, 333-361
26. Repin S., A priori error estimates of variational-difference methods for Hencky plasticity problems, Zap. Nauchn. Semin. POMI, 1995, 221, 226-234 (in Russian), English translation: J. Math. Sci., New York, 1997, 87(2), 3421-3427
27. Repin S.I., Errors of finite element methods for perfectly elasto-plastic problems, Math. Models Meth. Appl. Sci., 1996, 6(5), 587-604
28. Repin S., A posteriori estimates for approximate solutions of variational problems with strongly convex functionals, Problems of Mathematical Analysis, 1997, 17, 199-226 (in Russian), English translation: J. Math. Sci., 1999, 97(4), 4311-4328
29. Repin S., A posteriori error estimation for variational problems with uniformly convex functionals, Math. Comp., 2000, 69(230), 481-500
30. Repin S., A posteriori estimates for partial differential equations, Walter de Gruyter Verlag, Berlin, 2008
31. Repin S.I., Seregin G.A., Error estimates for stresses in the finite element analysis of the two-dimensional elastoplastic problems, Internat. J. Engrg. Sci., 1995, 33(2), 255-268
32. Repin S., Valdman J., Functional a posteriori error estimates for problems with nonlinear boundary conditions, J. Numer. Math., 2008, 16(1), 51-81
33. Repin S.I., Xanthis L.S., A posteriori error estimation for elasto-plastic problems based on duality theory, Comput. Methods Appl. Mech. Engrg., 1996, 138, 317-339
34. Seregin G., On the regularity of weak solutions of variational problems of plasticity theory, Algebra i Analiz, 1990, 2(2), 121-140 (in Russian), English translation: Leningrad Mathematical Journal, 1991, 2(2), 321-338
35. Simo J.C., Hughes T.J.R., Computational inelasticity, Springer-Verlag New York, 1998
36. Valdman J., Minimization of functional majorant in a posteriori error analysis based on H(div) multigrid-preconditioned CG method, Advances in Numerical Analysis, to appear
37. Wieners Ch., Nonlinear solution methods for infinitesimal perfect plasticity, ZAMM Z. Angew. Math. Mech., 2007, 87(8-9), 643-660