A splitting mixed covolume method for viscoelastic wave equations on triangular grids (Q2006926)

The authors propose a new splitting mixed covolume (SMCV) method for solving viscoelastic wave equations. The method combines the splitting positive definite mixed finite element (SPDMFE) and the mixed covolume (MCV) methods. One of the main features of this new scheme is that it does not require to solve the coupled system, thus reducing the scale of linear equations. This stems from the idea of SPDMFE. The semi-discrete and fully discrete SMCV schemes are established thanks to the introduction of a transfer operator. The existence and uniqueness for the semi-discrete scheme are justified. For both semi-discrete and fully discrete schemes, optimal a priori error estimates in different norms are proved. Some numerical tests are presented to show the efficiency of the method.