Abstract
ABSTRACT In this research, with help of the bilinear finite element, superconvergence analysis is proposed for nonlinear viscoelastic wave equation with strong damping. Firstly, a temporal discrete approximate scheme is established, and assisted by the method of first hypothesis and then proof, the temporal errors are given. Secondly, a new linearized second-order fully discrete scheme is presented, by using the technique of Interpolation and Ritz-prejection combination in the error estimations and analysis process, rigorous proofs are provided for the unconditional superclose estimates in -norm with order , here h and τ denote mesh size and time step, respectively. Finally, recurring to numerical examples, the correctness of the theoretical analysis is further demonstrated.
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