The diffusive-viscous wave equation arises in a variety of applications in geophysics, and it plays an important role in seismic exploration. In this paper, semi-discrete and fully discrete numerical methods are introduced to solve a general initial-boundary value problem of the diffusive-viscous wave equation. The spatial discretization is carried out through the finite element method, whereas the time derivatives are approximated by finite differences. Optimal order error estimates are derived for the numerical methods. Numerical results on a test problem are reported to illustrate the numerical convergence orders.

中文翻译：

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扩散粘性波动方程的数值分析

扩散粘性波动方程出现在地球物理学的各种应用中，在地震勘探中起着重要作用。本文介绍了半离散和全离散数值方法来求解扩散粘性波动方程的一般初边值问题。空间离散化是通过有限元方法进行的，而时间导数则是通过有限差分来近似的。为数值方法导出最优阶误差估计。报告了测试问题的数值结果以说明数值收敛顺序。