Perturbations of variational inequalities and rate of convergence of solutions

Pavel Doktor; Milan Kučera

Displaying similar documents to “Perturbations of variational inequalities and rate of convergence of solutions”

Shape optimization of an elasto-perfectly plastic body

Ivan Hlaváček (1987)

Aplikace matematiky

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Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise...

Approximations of parabolic variational inequalities

Alexander Ženíšek (1985)

Aplikace matematiky

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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...

Prox-regularization and solution of ill-posed elliptic variational inequalities

Alexander Kaplan, Rainer Tichatschke (1997)

Applications of Mathematics

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In this paper new methods for solving elliptic variational inequalities with weakly coercive operators are considered. The use of the iterative prox-regularization coupled with a successive discretization of the variational inequality by means of a finite element method ensures well-posedness of the auxiliary problems and strong convergence of their approximate solutions to a solution of the original problem. In particular, regularization on the kernel of the differential operator and...