Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations

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• 作者：Y. Zhao^a ; ^b ; Y. Zhang^a ; D. Shi^c ; F. Liu^b ; ^{f.liu@qut.edu.au" class="auth_mail" title="E-mail the corresponding author} ; I. Turner^b
• 关键词：Time-fractional diffusion equations ; Quasi-Wilson element ; L1L1 approximation ; Fully-discrete scheme ; Superclose and superconvergence
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：59
• 期：Complete
• 页码：38-47
• 全文大小：589 K

文摘

By means of spatial quasi-Wilson nonconforming finite element and classical L1$L1$ approximation, an unconditionally stable fully-discrete scheme for two-dimensional time fractional diffusion equations is established. Moreover, convergence results in L²$L^2$-norm and broken H¹$H^1$-norm and the corresponding superclose and superconvergence results in spatial direction in broken H¹$H^1$-norm are obtained by use of special properties of quasi-Wilson element. At the same time, the optimal order error estimate in temporal direction is derived by dealing with fractional derivative skillfully. Finally, numerical results demonstrate that the approximate scheme provides valid and efficient way for solving the time-fractional diffusion equation.