We introduce and analyze a stress-based formulation for Zener’s model in linear viscoelasticity. The method is aimed to tackle efficiently heterogeneous materials that admit purely elastic and viscoelastic parts in their composition.We write the mixed variational formulation of the problem in terms of a class of tensorial wave equation and obtain an energy estimate that guaranties the well-posedness of the problem through a standard Galerkin procedure. We propose and analyze mixed continuous and discontinuous Galerkin space discretizations of the problem and derive optimal error bounds for each semidiscrete solution in the corresponding energy norm. Finally, we discuss full discretization strategies for both Galerkin methods.

中文翻译：

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线性动力弹性-粘弹性复合结构的混合混合和混合不连续 Galerkin 方法

我们介绍并分析了线性粘弹性中 Zener 模型的基于应力的公式。该方法旨在有效地解决在其组成中允许纯弹性和粘弹性部分的异质材料。我们根据一类张量波动方程编写问题的混合变分公式，并获得保证适定性的能量估计通过标准的 Galerkin 程序解决问题。我们提出并分析问题的混合连续和不连续 Galerkin 空间离散化，并为相应能量范数中的每个半离散解导出最佳误差界限。最后，我们讨论了两种 Galerkin 方法的完全离散化策略。