A new splitting mixed covolume (SMCV) method is proposed for the viscoelastic wave equations by combining the splitting positive definite mixed finite element (SPDMFE) method with the mixed covolume (MCV) method. Based on the idea of the SPDMFE method, the difference between this method and the MCV method is that the proposed method does not need to solve the coupled system, thus reducing the scale of linear equations. By introducing a transfer operator, the semi-discrete and fully discrete SMCV schemes are proposed. The existence and uniqueness analysis of the semi-discrete scheme are given, and optimal a priori error estimates in different norm for these two schemes are derived. Finally, the feasibility and effectiveness of the proposed scheme are verified by some numerical results.

中文翻译：

---

三角网格上粘弹性波动方程的分裂混合体积法

提出了一种将分裂正定混合有限元（SPDMFE）方法与混合体积（MCV）方法相结合的粘弹性波动方程的新的分裂混合体积法（SMCV）。基于SPDMFE方法的思想，该方法与MCV方法的区别在于，该方法无需求解耦合系统，从而减小了线性方程的规模。通过引入转移算子，提出了半离散和完全离散的SMCV方案。给出了半离散方案的存在性和唯一性分析，并推导了这两种方案在不同范数下的最优先验误差估计。最后，通过一些数值结果验证了该方案的可行性和有效性。