A mixed finite element method with reduced symmetry for the standard model in linear viscoelasticity

We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following previous approach employed elastodynamics, present problem is formulated as second-order hyperbolic partial differential equation which, after using motion to eliminate displacement unknown, stress tensor remains main variable be found. The resulting variational formulation shown well-posed, class of $$\text {H}(\text {div})$$ -conforming semi-discrete schemes proved convergent. Then, we use Newmark trapezoidal rule obtain an associated fully discrete scheme, whose convergence results are also established. Finally, numerical examples illustrating performance reported.