Abstract
Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L^{1}(H^{1})-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order mathcal{O}(tau ^{2}+h^{m+1}) is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.
Highlights
In the recent few decades, the remarkable applications of fractional calculus in diverse engineering fields have been gradually realized and, the discussion of the related fractional partial differential equations (FPDEs) becomes a hot topic of many scholars
The numerical investigation of the FPDEs has been a vital topic in recent years
When solving approximation solutions for time FPDEs on the current time layer, one needs to retain the information about all the previous time layers, which makes the storage expensive
Summary
In the recent few decades, the remarkable applications of fractional calculus in diverse engineering fields have been gradually realized and, the discussion of the related fractional partial differential equations (FPDEs) becomes a hot topic of many scholars. Remark 4.2 In the present work, we obtain the superclose and superconvergence results in L1(H1)-norm through approach for WSDG fully discrete finite element scheme, which improve the conclusions in [17, 22, 29]. It seems that these results have never be seen in the existing literature. Is sufficient but unnecessary for the numerical accuracy of the proposed schemes In this example, we are concerned with the computational results of the fully finite element scheme for the cases β = 2, 3/2, 1, respectively.
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