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Papers by Jaroslav Haslinger

Research paper thumbnail of Optimal control of variational inequalities. Approximation theory and numerical realization

Applied Mathematics & Optimization, 1986

An optimal-control problem of a variational inequality of the elliptic type is investigated. The ... more An optimal-control problem of a variational inequality of the elliptic type is investigated. The problem is approximated by a family of finite-dimensional problems and the convergence of the approximated optimal controls is shown. The finite-dimensional problems, being nonsmooth, are to be optimized by a bundle algorithm, which requires an element of Clarke's generalized gradient of the minimized function. A simple algorithm which yields this element is proposed. Some numerical experiments with a simple model problem have also been carried out.

Research paper thumbnail of Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

Journal of Fluids Engineering, 2016

Research paper thumbnail of Least square method for solving contact problems with friction obeying the Coulomb law

Research paper thumbnail of Semi-smooth Newton method for Solving Unilateral Problems in Fictitious Domain Formulations

SNA'08, Liberec •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit OUTLINE Motivation Fi... more SNA'08, Liberec •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit OUTLINE Motivation Fictitious domain formulation Algorithm -Semi-Smooth Newton method Inner solvers Numerical experiments •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit OUTLINE Motivation Fictitious domain formulation Algorithm -Semi-Smooth Newton method Inner solvers Numerical experiments •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit FDM for Dirichlet problem:

Research paper thumbnail of Sur la solution d’un problème de la plaque

Research paper thumbnail of Shape Optimization of Elasto-Plastic Bodies in Contact

Research paper thumbnail of Stokes problem with a solution dependent slip bound: Stability of solutions with respect to domains

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2016

We study the Stokes problem in a bounded planar domain Ω with a friction type boundary condition ... more We study the Stokes problem in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the velocity field. Besides the usual velocity-pressure formulation, we introduce an alternative formulation with three Lagrange multipliers which allows a more flexible treatment of the impermeability condition as well as optimum design problems with cost functions depending on the shear and/or normal stress. Our main goal is to determine under which conditions concerning smoothness of Ω, solutions to the Stokes system depend continuously on variations of Ω.

Research paper thumbnail of Approximation of optimal control problems of hemivariational inequalities

Numerical Functional Analysis and Optimization, 1992

The existence of a solution of a hemivariational inequality is proved and the full discretization... more The existence of a solution of a hemivariational inequality is proved and the full discretization of it is discussed. Then we study the approximation of the optimal control problem, the state relation of which is done by the hemivariational inequality.

Research paper thumbnail of Optimal Control of Systems Governed By Hemivariational Inequalities

Research paper thumbnail of Shape Optimization for Navier–Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

Applied Mathematics & Optimization, 2011

We study the shape optimization problem for the paper machine headbox which distributes a mixture... more We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

Research paper thumbnail of Finite Element Approximation of Hemivariational Inequalities

Journal of Global Optimization, 2000

ABSTRACT

Research paper thumbnail of Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

Applied Mathematics and Optimization, Feb 13, 2009

We study the shape optimization problem for the paper machine headbox which distributes a mixture... more We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

Research paper thumbnail of Variational Inequalities: F. E. Approach

Research paper thumbnail of Signorini problem with Coulomb's law of friction. Shape optimization in contact problems

International Journal For Numerical Methods in Engineering, Mar 15, 1992

Research paper thumbnail of Finite Element Approximation of Vector-Valued Hemivariational Problems

Journal of Global Optimization, 1997

In this paper we develop a finite element approximation for vector-valued hemivariational inequal... more In this paper we develop a finite element approximation for vector-valued hemivariational inequalities. This class of hemivariational problems was introduced in [12], . We study two different problems: unconstrained one and constrained one with a nonempty, closed, convex constraint set K.

Research paper thumbnail of Contact between elastic bodies. III. Dual finite element analysis

Research paper thumbnail of Shape differentiability of the solution to a fictitious domain formulation

Research paper thumbnail of Domain Optimization Problem Governed by a State Inequality with a �Flux'' Cost Functional

Zamm Zeitschrift Fur Angewandte Mathematik Und Mechanik, 1986

Shape optimization with a state unilateral boundary value probleni nnd th.e flux cost functional ... more Shape optimization with a state unilateral boundary value probleni nnd th.e flux cost functional is analyzed. Uaing the pennlty method the existence of n solution is proved. U iiacrom~e8 p a 6 o~e paccMaTpusaeTcH aanasa cyuccTnosaHMR onTmaJibHot4 06nac.r~ B npobnenrax, ICOTOplJe J'lIpaBJlfllOTCH CUCTt !MaMM OIIMChlBaeMb1%l1.I OnHOCTOPOHHl rl MM rPaHllYllhlMM 3aAallaMU.

Research paper thumbnail of On the approximation of the Signorini problem with friction

Research paper thumbnail of Contact problem with friction

Research paper thumbnail of Optimal control of variational inequalities. Approximation theory and numerical realization

Applied Mathematics & Optimization, 1986

An optimal-control problem of a variational inequality of the elliptic type is investigated. The ... more An optimal-control problem of a variational inequality of the elliptic type is investigated. The problem is approximated by a family of finite-dimensional problems and the convergence of the approximated optimal controls is shown. The finite-dimensional problems, being nonsmooth, are to be optimized by a bundle algorithm, which requires an element of Clarke's generalized gradient of the minimized function. A simple algorithm which yields this element is proposed. Some numerical experiments with a simple model problem have also been carried out.

Research paper thumbnail of Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

Journal of Fluids Engineering, 2016

Research paper thumbnail of Least square method for solving contact problems with friction obeying the Coulomb law

Research paper thumbnail of Semi-smooth Newton method for Solving Unilateral Problems in Fictitious Domain Formulations

SNA'08, Liberec •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit OUTLINE Motivation Fi... more SNA'08, Liberec •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit OUTLINE Motivation Fictitious domain formulation Algorithm -Semi-Smooth Newton method Inner solvers Numerical experiments •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit OUTLINE Motivation Fictitious domain formulation Algorithm -Semi-Smooth Newton method Inner solvers Numerical experiments •First •Prev •Next •Last •Go Back •Full Screen •Close •Quit FDM for Dirichlet problem:

Research paper thumbnail of Sur la solution d’un problème de la plaque

Research paper thumbnail of Shape Optimization of Elasto-Plastic Bodies in Contact

Research paper thumbnail of Stokes problem with a solution dependent slip bound: Stability of solutions with respect to domains

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2016

We study the Stokes problem in a bounded planar domain Ω with a friction type boundary condition ... more We study the Stokes problem in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the velocity field. Besides the usual velocity-pressure formulation, we introduce an alternative formulation with three Lagrange multipliers which allows a more flexible treatment of the impermeability condition as well as optimum design problems with cost functions depending on the shear and/or normal stress. Our main goal is to determine under which conditions concerning smoothness of Ω, solutions to the Stokes system depend continuously on variations of Ω.

Research paper thumbnail of Approximation of optimal control problems of hemivariational inequalities

Numerical Functional Analysis and Optimization, 1992

The existence of a solution of a hemivariational inequality is proved and the full discretization... more The existence of a solution of a hemivariational inequality is proved and the full discretization of it is discussed. Then we study the approximation of the optimal control problem, the state relation of which is done by the hemivariational inequality.

Research paper thumbnail of Optimal Control of Systems Governed By Hemivariational Inequalities

Research paper thumbnail of Shape Optimization for Navier–Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

Applied Mathematics & Optimization, 2011

We study the shape optimization problem for the paper machine headbox which distributes a mixture... more We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

Research paper thumbnail of Finite Element Approximation of Hemivariational Inequalities

Journal of Global Optimization, 2000

ABSTRACT

Research paper thumbnail of Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

Applied Mathematics and Optimization, Feb 13, 2009

We study the shape optimization problem for the paper machine headbox which distributes a mixture... more We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

Research paper thumbnail of Variational Inequalities: F. E. Approach

Research paper thumbnail of Signorini problem with Coulomb's law of friction. Shape optimization in contact problems

International Journal For Numerical Methods in Engineering, Mar 15, 1992

Research paper thumbnail of Finite Element Approximation of Vector-Valued Hemivariational Problems

Journal of Global Optimization, 1997

In this paper we develop a finite element approximation for vector-valued hemivariational inequal... more In this paper we develop a finite element approximation for vector-valued hemivariational inequalities. This class of hemivariational problems was introduced in [12], . We study two different problems: unconstrained one and constrained one with a nonempty, closed, convex constraint set K.

Research paper thumbnail of Contact between elastic bodies. III. Dual finite element analysis

Research paper thumbnail of Shape differentiability of the solution to a fictitious domain formulation

Research paper thumbnail of Domain Optimization Problem Governed by a State Inequality with a �Flux'' Cost Functional

Zamm Zeitschrift Fur Angewandte Mathematik Und Mechanik, 1986

Shape optimization with a state unilateral boundary value probleni nnd th.e flux cost functional ... more Shape optimization with a state unilateral boundary value probleni nnd th.e flux cost functional is analyzed. Uaing the pennlty method the existence of n solution is proved. U iiacrom~e8 p a 6 o~e paccMaTpusaeTcH aanasa cyuccTnosaHMR onTmaJibHot4 06nac.r~ B npobnenrax, ICOTOplJe J'lIpaBJlfllOTCH CUCTt !MaMM OIIMChlBaeMb1%l1.I OnHOCTOPOHHl rl MM rPaHllYllhlMM 3aAallaMU.

Research paper thumbnail of On the approximation of the Signorini problem with friction

Research paper thumbnail of Contact problem with friction