Optimization of conducting structures by using the homogenization method

Approximation and numerical realization of a class of optimization problems with control variables represented by coefficients of linear elliptic state equations is considered. Convergence analysis of well-posed problems is performed by using one- and two-level approximation strategies. The latter is utilized in an optimization layout problem for two conductive constituents, for which the necessary steps to transfer the well-posed problem into a computational form are described and some numerical experiments are given.

Finite element approximation of parabolic hemivariational inequalities

In this paper we introduce a finite element approximation for a parabolic hemivariational initial boundary value problem. We prove that the approximate problem is solvable and its solutions converge on subsequences to the solutions of the continuous problem

Hemivariational Inequalities and Hysteresis

Hemivariational inequalities introduced by P.D. Panagiotopoulos are generalizations of variational inequalities. This type of inequality problems arises, e.g. in variational formulation of mechanical problems whenever nonmonotone and multivalued relations or nonconvex energy functions are involved. Typical examples of such kind of phenomena are nonmonotone friction laws and adhesive contact laws. Mathematically these nonmonotone relations are described by means of generalized gradients (in sense of F.H. Clarke) of nonconvex potential functions. For applications and for their mathematical treatment we refer to [9],[10],[13]–[18].

On parabolic hemivariational inequalities and applications