×

Finite element approximation of a coupled contact Stefan-like problem arising from the time discretization in deformation theory of thermo-plasticity. (English) Zbl 0891.73066

Summary: We give a mathematical formulation of the coupled contact Stefan-like problem in deformation theory of plasticity, which arises from the discretization in time. The problem leads to solving the system of variational inequalities, which is approximated by the FEM. Numerical analysis of the problem is made.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74L05 Geophysical solid mechanics
80A22 Stefan problems, phase changes, etc.
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barbu, V., Nonlinear Semigroup and Differential Equations in Banach Spaces (1976), Noordhoff, Leyden
[2] Céa, J., Optimisation, théorie et algorithmes (1971), Dunod: Dunod Paris · Zbl 0211.17402
[3] Ciarlet, P., The Finite Element Method for Elliptic Problems (1978), North-Holland: North-Holland Amsterdam
[4] Ciavaldini, J. F., Analyse numérique d’un probléme de Stefan á deux phases par un méthod d’éléments finis, SIAM J. Numer. Anal., 12, 464-489 (1975) · Zbl 0272.65101
[5] Ekeland, I.; Temam, R., Convex Analysis and Variational Problems (1976), North-Holland: North-Holland Amsterdam
[6] Elliott, C. M., On the finite element approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem, IMA J. Numer. Anal., 1, 115-125 (1981) · Zbl 0469.65042
[7] Falk, R. S., Error estimates for approximation of a class of variational inequalities, Math. Comput., 28, 963-971 (1974) · Zbl 0297.65061
[8] Fučík, S.; Kratochvíl, A.; Nečas, J., Kačanov’s method and its applications, Rev. Roumaine Math. Pures Appl., 20, 8, 909-915 (1975)
[9] Glowinski, R., Finite elements and variational inequalities, (Whiteman, J. R., The Mathematics of Finite Elements and Applications III (1979), Academic Press: Academic Press New York), 135-171 · Zbl 0442.65056
[10] Nečas, J.; Hlaváček, I., Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction (1981), Elsevier: Elsevier Amsterdam · Zbl 0448.73009
[11] Nečas, J.; Hlaváček, I., Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modulus method, Appl. Math., 28, 3, 199-214 (1983) · Zbl 0512.73097
[12] Nedoma, J., On one type of Signorini problem without friction in linear thermoelasticity, Appl. Math., 28, 6, 393-407 (1983) · Zbl 0534.73095
[13] Nedoma, J., On the Signorini problem with friction in linear thermoelasticity: the quasi-coupled 2D-case, Appl. Math., 32, 3, 186-199 (1987) · Zbl 0631.73098
[14] Nedoma, J., Finite element analysis of contact problems in thermoelasticity. The semi-coercive case, J. Comput. Appl. Math., 50, 411-423 (1994) · Zbl 0804.73069
[15] Nedoma, J., Equations of magnetodynamics of incompressible thermo-Binhgam’s fluid under the gravity effect, J. Comput. Appl. Math., 59, 109-128 (1995) · Zbl 0831.76096
[16] Nedoma, J., Numerical solutions of coupled two-phase Stefan-contact problems with friction in linear thermoelasticity by variational inequalities. The coercive case, (Technical Report No. 675 (1996), ICS AS CR: ICS AS CR Prague)
[17] Nedoma, J.; Dvořák, J., On the FEM solution of a coupled contact-two-phase Stefan problem in thermo-elasticity. Coercive case, J. Comput. Appl. Math., 63, 411-420 (1995) · Zbl 0852.73067
[18] Raviart, P. A., The use of numerical integration in finite element methods for solving parabolic equations, (Conf. on Numerical Analysis (1972), Royal Irish Academy: Royal Irish Academy Dublin) · Zbl 0293.65086
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.