@article {IOPORT.04172290,
    author       = {Bertoluzza, S.},
    title        = {Discretization of parabolic inequalities.},
    year         = {1989},
    journal      = {Calcolo},
    volume       = {26},
    number       = {2-4},
    issn         = {0008-0624},
    pages        = {237-266},
    publisher    = {Istituto Nazionale delle Ricerche, Istituto di Matematica Computazionale, Pisa; Springer-Verlag Italia, Milano},
    doi          = {10.1007/BF02575731},
    abstract     = {The paper deals with time discretization of abstract parabolic variational inequalities where linear multistep methods are used. The problems under consideration are the following: Let H, V be two complex Hilbert spaces $(V\subset H\subset V')$ and K a closed subset of V. Given $u\sb 0\in K$, $f: [0,T]\to V',\quad A: K\to V'.$ Find a function $u: [0,T]\to K$ such that $u,u'\in L\sb{\infty}([0,T],H)\cap L\sb 2([0,T],H),\quad u(0)=u\sb 0$ and $Re(u'(t)+Au(t)-f(t),\quad u(t)-v)\le 0\forall v\in K$ or $$ \int\sp{\infty}\sb{0}(w(t)+Au(t)-f(t),\quad u(t)- v(t))dt\le \vert u\sb 0-v(0)\vert\sp 2 $$ for all $v,w\in L\sb{\infty}([0,T],H)\cap L\sb 2([0,T],H),$ respectively. The author considers three different versions of discretizations in order to make easier (i) the manipulation of the inequality, or (ii) the control of stability, or (iii) the application of Baiocchi's technique. Some new definitions are introduced. The so-called ($\sigma$,$\tau$)- compatibility of certain bilinear forms is discussed. Error estimations are given. The discretization of a model problem with the heat operator illustrates the theory Numerical results are presented for this example.},
    reviewer     = {W.H.Schmidt},
    identifier   = {04172290},
}