On the MGT-micropolar viscoelasticity

Abstract

In this short paper we analyze, from both analytical and numerical points of view, a dynamic problem arising in micropolar viscoelasticity. An existence and uniqueness result is proved by using the theory of linear semigroups. The exponential decay of the solution is also shown. Then, by using the finite element method and the implicit Euler scheme, a fully discrete approximation is introduced. A priori error estimates are proved, from which the linear convergence is derived under adequate additional regularity conditions. Finally, a one-dimensional numerical example is presented to show the accuracy of the approximation.