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We introduce and analyze a new mixed finite element method with reducedsymmetry for the standard linear model in viscoelasticity. Following a previousapproach employed for linear elastodynamics, the present problem is formulatedas a second-order hyperbolic partial differential equation in which, afterusing the motion equation to eliminate the displacement unknown, the stresstensor remains as the main variable to be found. The resulting variationalformulation is shown to be well-posed, and a class of$\text{H}(\text{div})$-conforming semi-discrete schemes is proved to beconvergent. Then, we use the Newmark trapezoidal rule to obtain an associatedfully discrete scheme, whose main convergence results are also established.Finally, numerical examples illustrating the performance of the method arereported.

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