The optimal error estimate and superconvergence of the local discontinuous Galerkin methods for one-dimensional linear fifth order time dependent equations

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• 作者：Hui Bi ; ^{bi_hui2002@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Chengeng Qian ^{qiancg@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yang Sun ^{sunysy@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Local discontinuous Galerkin method ; Superconvergence ; Error estimate
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：72
• 期：3
• 页码：687-703
• 全文大小：476 K

文摘

In this paper, we investigate the optimal error estimate and the superconvergence of linear fifth order time dependent equations. We prove that the local discontinuous Galerkin (LDG) solution is i35" class="mathmlsrc">i35.gif&_user=111111111&_pii=S089812211630298X&_rdoc=1&_issn=08981221&md5=a54fc5cb595f5369897452fdaf90d9e6" title="Click to view the MathML source">(k+1)th order convergent when the piecewise i36" class="mathmlsrc">i36.gif&_user=111111111&_pii=S089812211630298X&_rdoc=1&_issn=08981221&md5=b7294b59ddbfaf24b1131737f9985a82" title="Click to view the MathML source">P^k space is used. Also, the numerical solution is i37" class="mathmlsrc">i37.gif&_user=111111111&_pii=S089812211630298X&_rdoc=1&_issn=08981221&md5=c01ac2026c2844eee7b2ae1ee5d822d4">lineImage" height="21" width="49" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S089812211630298X-si37.gif">th order superconvergent to a particular projection of the exact solution. The numerical experiences indicate that the order of the superconvergence is i38" class="mathmlsrc">i38.gif&_user=111111111&_pii=S089812211630298X&_rdoc=1&_issn=08981221&md5=355d3358ab586d7596c8c90ec6a4c4ec" title="Click to view the MathML source">(k+2), which implies the result obtained in this paper is suboptimal.