Splitting positive definite mixed element method for viscoelasticity wave equation (Q1758135)

The authors propose here a splitting positive definite finite element scheme based on certain transformation (cf. [\textit{L. Gao; D. Liang} and \textit{Bo Zhang}, Math. Methods Appl. Sci. 27, No. 17, 1997--2016 (2004; Zbl 1071.65129)]) for viscoelasticity wave equations. The proposed procedure can be split into three independent symmetric positive definite integro-differential sub-system and does not need to solve a coupled system of equations, Error estimates for both semidiscrete and fully discrete schemes have been obtained and the existence and uniqueness of semidiscrete scheme have been shown.