This paper considers semi-discrete and fully discrete mixed finite element discretizations for Maxwell-model-based problems of wave propagation in 2-dimensional linear viscoelastic solid. A large class of existing mixed conforming finite elements for elasticity are used in the spatial discretization. In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of displacement and stress. Error estimates of the two schemes, as well as an unconditional stability result for the fully discrete scheme, are derived. Numerical experiments are provided which apply two low order rectangular elements in the spatial discretization.

翻译：本文论述基于模型的马克斯韦尔在2维线性粘结固体中波波传播问题的半分异和完全离散的混合有限元素分解。在空间离散中,使用大量现有混合的符合弹性的有限元素。在完全离散的方案中,采用了离散-尼科尔森方案,以近似移位和压力的暂时衍生物。得出了两种方法的错误估计,以及完全离散方案的无条件稳定性结果。提供了数字实验,在空间离散中应用两个低顺序矩形元素。