The principal aim of this work is to provide an adapted numerical scheme for the approximation of elastic wave propagation in incompressible solids. We rely on high-order conforming finite element with mass lumping for space discretisation and implicit/explicit, second-order, energy-preserving time discretisation. The time step restriction only depends on the shear wave velocity and at each time step a Poisson problem must be solved to account for the incompressibility constraint that is imposed by penalisation techniques.

中文翻译：

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不可压缩弹性动力学方程半隐式时间离散化的保守惩罚策略

这项工作的主要目的是为不可压缩固体中的弹性波传播提供近似的数值方案。我们依靠具有质量集总的高阶一致有限元进行空间离散化和隐式/显式，二阶，节能时间离散化。时间步长限制仅取决于剪切波速度，并且在每个时间步长都必须解决泊松问题，以解决惩罚技术施加的不可压缩性约束。