A fully discrete two-grid finite element method for nonlinear hyperbolic integro-differential equation

作者：

Highlights：

• The optimal error estimates in H1-norm are derived in both continuous-time scheme and fully discrete scheme.

• The optimal convergence order can be derived when the coarse-grid of size H and the fine-grid of size h satisfy h=O(H2).

• Two-grid finite element methods can reduce the storage, save a large amount of time and maintain the numerical precision.

摘要

•The optimal error estimates in H1-norm are derived in both continuous-time scheme and fully discrete scheme.•The optimal convergence order can be derived when the coarse-grid of size H and the fine-grid of size h satisfy h=O(H2).•Two-grid finite element methods can reduce the storage, save a large amount of time and maintain the numerical precision.

论文关键词：Nonlinear hyperbolic integro-differential equation,Two-grid,Finite element method,Fully discrete scheme,Error estimate

论文评审过程：Received 15 April 2021, Revised 7 August 2021, Accepted 14 August 2021, Available online 30 August 2021, Version of Record 30 August 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126596