Abstract
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.
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