Finite element approximation of a coupled contact Stefan-like problem arising from the time discretization in deformation theory of thermo-plasticity

Barbu, 1976 Céa, 1971 Ciarlet, 1978 Ciavaldini, 1975, Analyse numérique d'un probléme de Stefan á deux phases par un méthod d'éléments finis, SIAM J. Numer. Anal., 12, 464, 10.1137/0712037 Ekeland, 1976 Elliott, 1981, 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, 10.1093/imanum/1.1.115 Falk, 1974, Error estimates for approximation of a class of variational inequalities, Math. Comput., 28, 963, 10.1090/S0025-5718-1974-0391502-8 Fučík, 1975, Kačanov's method and its applications, Rev. Roumaine Math. Pures Appl., 20, 909 Glowinski, 1979, Finite elements and variational inequalities, 135 Nečas, 1981 Nečas, 1983, Solution of Signorini's contact problem in the deformation theory of plasticity by secant modulus method, Appl. Math., 28, 199, 10.21136/AM.1983.104027 Nedoma, 1983, On one type of Signorini problem without friction in linear thermoelasticity, Appl. Math., 28, 393, 10.21136/AM.1983.104053 Nedoma, 1987, On the Signorini problem with friction in linear thermoelasticity: the quasi-coupled 2D-case, Appl. Math., 32, 186, 10.21136/AM.1987.104250 Nedoma, 1994, Finite element analysis of contact problems in thermoelasticity. The semi-coercive case, J. Comput. Appl. Math., 50, 411, 10.1016/0377-0427(94)90317-4 Nedoma, 1995, Equations of magnetodynamics of incompressible thermo-Binhgam's fluid under the gravity effect, J. Comput. Appl. Math., 59, 109, 10.1016/0377-0427(94)00019-W Nedoma, 1996, Numerical solutions of coupled two-phase Stefan-contact problems with friction in linear thermoelasticity by variational inequalities. The coercive case Nedoma, 1995, On the FEM solution of a coupled contact-two-phase Stefan problem in thermo-elasticity. Coercive case, J. Comput. Appl. Math., 63, 411, 10.1016/0377-0427(95)00091-7 Raviart, 1972, The use of numerical integration in finite element methods for solving parabolic equations