A Two-Grid Algorithm of Fully Discrete Galerkin Finite Element Methods for a Nonlinear Hyperbolic Equation
Year: 2020
Author: Kang Li, Zhijun Tan
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 1050–1067
Abstract
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 $H^1$-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0200
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 1050–1067
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonlinear hyperbolic equation two-grid algorithm finite element method fully discrete error estimate.
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