An optimized finite element extrapolating method for 2D viscoelastic wave equation

In this study, we first present a classical finite element (FE) method for a two-dimensional (2D) viscoelastic wave equation and analyze the existence, stability, and convergence of the FE solutions. Then we establish an optimized FE extrapolating (OFEE) method based on a proper orthogonal decomposi...

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Detalles Bibliográficos
Autores principales: Xia, Hong, Luo, Zhendong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5596059/
https://www.ncbi.nlm.nih.gov/pubmed/28979080
http://dx.doi.org/10.1186/s13660-017-1496-7
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author Xia, Hong
Luo, Zhendong
author_facet Xia, Hong
Luo, Zhendong
author_sort Xia, Hong
collection PubMed
description In this study, we first present a classical finite element (FE) method for a two-dimensional (2D) viscoelastic wave equation and analyze the existence, stability, and convergence of the FE solutions. Then we establish an optimized FE extrapolating (OFEE) method based on a proper orthogonal decomposition (POD) method for the 2D viscoelastic wave equation and analyze the existence, stability, and convergence of the OFEE solutions and furnish the implement procedure of the OFEE method. Finally, we furnish a numerical example to verify that the numerical computing results correspond with the theoretical ones. This signifies that the OFEE method is feasible and efficient for solving the 2D viscoelastic wave equation.
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spelling pubmed-55960592017-10-02 An optimized finite element extrapolating method for 2D viscoelastic wave equation Xia, Hong Luo, Zhendong J Inequal Appl Research In this study, we first present a classical finite element (FE) method for a two-dimensional (2D) viscoelastic wave equation and analyze the existence, stability, and convergence of the FE solutions. Then we establish an optimized FE extrapolating (OFEE) method based on a proper orthogonal decomposition (POD) method for the 2D viscoelastic wave equation and analyze the existence, stability, and convergence of the OFEE solutions and furnish the implement procedure of the OFEE method. Finally, we furnish a numerical example to verify that the numerical computing results correspond with the theoretical ones. This signifies that the OFEE method is feasible and efficient for solving the 2D viscoelastic wave equation. Springer International Publishing 2017-09-12 2017 /pmc/articles/PMC5596059/ /pubmed/28979080 http://dx.doi.org/10.1186/s13660-017-1496-7 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Xia, Hong
Luo, Zhendong
An optimized finite element extrapolating method for 2D viscoelastic wave equation
title An optimized finite element extrapolating method for 2D viscoelastic wave equation
title_full An optimized finite element extrapolating method for 2D viscoelastic wave equation
title_fullStr An optimized finite element extrapolating method for 2D viscoelastic wave equation
title_full_unstemmed An optimized finite element extrapolating method for 2D viscoelastic wave equation
title_short An optimized finite element extrapolating method for 2D viscoelastic wave equation
title_sort optimized finite element extrapolating method for 2d viscoelastic wave equation
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5596059/
https://www.ncbi.nlm.nih.gov/pubmed/28979080
http://dx.doi.org/10.1186/s13660-017-1496-7
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