论文标题
在线性粘弹性中标准模型的混合有限元法和对称性降低
A mixed finite element method with reduced symmetry for the standard model in linear viscoelasticity
论文作者
论文摘要
我们介绍并分析了一种新的混合有限元方法，其中具有降低的对称性的粘弹性线性模型。遵循先前用于线性弹性动力学的方法，将目前的问题提出为二阶双曲偏微分方程，在使用运动方程式消除位移未知之后，应力张量仍然是要找到的主要变量。结果表明，所产生的变分配方被证明是良好的，并且证明了$ \ text {h}（\ text {div}）$ - 符合半差异方案的类别被证明是收敛的。然后，我们使用Newmark梯形规则获得相关的完全离散方案，该方案还建立了其主要收敛结果。最后，报道了该方法性能的数值示例。
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.
