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

Zhijun Tan, Kang Li and Yanping Chen

Applied Mathematics and Computation, 2022, vol. 413, issue C

Abstract: Two-grid fully discrete finite element approximations of the solution for a nonlinear hyperbolic integro-differential equation are considered and analyzed in this paper. The H1-norm error estimate is derived, which shows that the optimal convergence order can be obtained when the coarse-grid of size H and the fine-grid of size h satisfy h=O(H2). Besides reducing the storage and saving a large amount of time, two-grid methods also keep the accuracy of convergence in calculations. Numerical examples are given to support our theoretical results and demonstrate the efficiency of the methods.

Keywords: Nonlinear hyperbolic integro-differential equation; Two-grid; Finite element method; Fully discrete scheme; Error estimate (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321006809

DOI: 10.1016/j.amc.2021.126596

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