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

针对粘弹性的标准线性模型，我们引入并分析了一种新的具有减少对称性的混合有限元方法。遵循先前用于线性弹性动力学的方法，当前问题被公式化为二阶双曲偏微分方程，其中，在使用运动方程消除未知位移之后，应力张量仍然是要发现的主要变量。结果表明，变分公式的位置很好，并且有一类\（\ text {H}（\ text {div}）\）符合半离散方案被证明是收敛的。然后，我们使用Newmark梯形法则来获得相关的完全离散方案，并建立了其主要收敛结果。最后，报告了说明该方法性能的数值示例。