@article{Yang2024, 
author = {Yining Yang and Cao Wen and Yang Liu and Hong Li and Jinfeng Wang},
title = {Optimal time two-mesh mixed finite element method for a nonlinear fractional hyperbolic wave model},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {1},
pages = {24-52},
keywords = {fractional hyperbolic wave model, time two-mesh mixed finite element method, WSGD operator, error estimates},
url = {https://www.sciopen.com/article/10.3934/cam.2024002},
doi = {10.3934/cam.2024002},
abstract = {In this article, a second-order time discrete algorithm with a shifted parameter  θ combined with a fast time two-mesh (TT-M) mixed finite element (MFE) scheme was considered to look for the numerical solution of the nonlinear fractional hyperbolic wave model. The second-order backward difference formula including a shifted parameter  θ (BDF2- θ) with the weighted and shifted Grünwald difference (WSGD) approximation for fractional derivative was used to discretize time direction at time  tn−θ, the  H1-Galerkin MFE method was applied to approximate the spatial direction, and the fast TT-M method was used to save computing time of the developed MFE system. A priori error estimates for the fully discrete TT-M MFE system were analyzed and proved in detail, where the second-order space-time convergence rate in both  L2-norm and  H1-norm were derived. Detailed numerical algorithms with smooth and weakly regular solutions were provided. Finally, some numerical examples were provided to illustrate the feasibility and effectiveness for our scheme.}
}