Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...

The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by Kelvin–Voigt model with fractional time derivatives. For this purpose, theory two-scale convergence and Laplace transform respect are used. It shown that partial integro-differential derivatives exponential convolution kernels. In order find coefficients kernels th...

Abstract It is shown that the solution to boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon parameters, viscosity, and viscoelastic coefficients. Convergence also shown.

In this paper we present results on existence and regularity of integral representations of feedback operators arising from hyperbolic PDE control problems. The existence of such representations is important for the design of low order compensators and for the placement of sensors. This paper contains results which apply to problems with spatial domains in N dimensions. Numerical examples are i...

Abstract: We study optimal control of systems governed by a coupled system of hemivariational inequalities, modeling a dynamic thermoviscoelastic problem, which describes frictional contact between a body and a foundation. We employ the Kelvin-Voigt viscoelastic law, include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions. We consider...

Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...