Application of Rothe's method to parabolic variational inequalities

Igor Bock; Jozef Kačur

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The paper deals with an initial problem of a parabolic variational inequality whichcontains a nonlinear elliptic form $a (v, w)$ having a potential $J (v)$ , which is twice $G$ -differentiable at arbitrary $v \in H^{1} (Ω)$ . This property of $a (v, w)$ makes it possible to prove convergence of an approximate solution defined by a linearized scheme which is fully discretized - in space by the finite elements method and in time by a one-step finite-difference method. Strong convergence of the approximate solution is proved without...