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A New Error Analysis of Nonconforming $EQ^{rot}_1$ FEM for Nonlinear BBM Equation

A New Error Analysis of Nonconforming $EQ^{rot}_1$ FEM for Nonlinear BBM Equation
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Year:    2018

Author:    Yanhua Shi, Yanmin Zhao, Fenling Wang, Dongyang Shi

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 5 : pp. 1227–1246

Abstract

Nonconforming $EQ^{rot}_1$ element is applied to solving a kind of nonlinear Benjamin-Bona-Mahony (BBM for short) equation both for space-discrete and fully discrete schemes. A new important estimate is proved, which improves the result of previous works with the exact solution $u$ belonging to $H^2(Ω)$ instead of $H^3(Ω)$. And then, the supercloseness and global superconvergence estimates in broken $H^1$ norm are obtained for space-discrete scheme. Further, the superclose estimates are deduced for backward Euler and Crank-Nicolson schemes. To confirm our theoretical analysis, numerical experiments for backward Euler scheme are executed. It seems that the results presented herein have never been seen for nonconforming FEMs in the existing literature.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2017-0264

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 5 : pp. 1227–1246

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:   

Author Details

Yanhua Shi

Yanmin Zhao

Fenling Wang

Dongyang Shi

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