@Article{NMTMA-13-4,
author = {Li, Kang and Zhijun, Tan},
title = {A Two-Grid Algorithm of Fully Discrete Galerkin Finite Element Methods for a Nonlinear Hyperbolic Equation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {4},
pages = {1050--1067},
abstract = {<p style="text-align: justify;">A two-grid finite element approximation is studied in the fully discrete
scheme obtained by discretizing in both space and time for a nonlinear hyperbolic
equation. The main idea of two-grid methods is to use a coarse-grid space ($S_H$) to
produce a rough approximation for the solution of nonlinear hyperbolic problems
and then use it as the initial guess on the fine-grid space ($S_h$). Error estimates are
presented in $H<span style="font-size: 13.3333px;">^1$</span>-norm, which show that two-grid methods can achieve the optimal
convergence order as long as the two different girds satisfy $h$ = $\mathcal{O}$($H^2$). With the
proposed techniques, we can obtain the same accuracy as standard finite element
methods, and also save lots of time in calculation. Theoretical analyses and numerical examples are presented to confirm the methods.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0200},
url = {https://global-sci.com/article/90380/a-two-grid-algorithm-of-fully-discrete-galerkin-finite-element-methods-for-a-nonlinear-hyperbolic-equation}
}