A mixed parameter formulation with applications to linear viscoelastic slender structures

Abstract

We present the analysis of an abstract parameter-dependent  mixed variational formulation based on Volterra integrals of second kind. Adapting the classic mixed theory in the Volterra equations setting, we prove the well posedness of the resulting system. Stability and error estimates are derived, where all the estimates are independent of the perturbation parameter. We  provide applications of the developed analysis  for a viscoelastic Timoshenko beam and report numerical tests for this problem. We also comment, numerically, the performance of a viscoelastic Reissner-Mindlin plate.