Superconvergence analysis for nonlinear viscoelastic wave equation with strong damping

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 $H^1$-norm with order $O\left(h^2+{\tau }^2\right)$, 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.

KEYWORDS:

• Nonlinear viscoelastic wave equation
• bilinear finite element
• second-order fully discrete scheme
• unconditional superconvergence results

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N15
• 65N30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by National Natural Science Foundation of China (NSFC) [project numbers 11671369,12071443] and Key Scientific Research Project of Colleges and Universities in Henan Province [grant number 22B110008].