Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing mixed conforming finite elements for elasticity in the spatial discretization. In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables. Error estimates of the semi-discrete and fully discrete schemes, as well as an unconditional stability result for the fully discrete scheme, are derived. Numerical experiments are provided to verify the theoretical results.

翻译：考虑采用半分异和完全离散的混合有限元素方法,处理基于模型的马克斯韦尔在线性粘弹性固体中波波传播问题。这一混合有限元素框架允许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,为压力和速度变量的暂时衍生物的近似采用了克朗-尼科尔森办法。半分异和完全离散的系统错误估计,以及完全离散的系统无条件的稳定结果。提供了数字实验,以核实理论结果。