2025
DOI: 10.4208/jcm.2210-m2022-0085
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Reconstruction-Based a Posteriori Error Estimates for the L1 Method for Time Fractional Parabolic Problems

Jiliang Cao,
Aiguo Xiao null,
Wansheng Wang

Abstract: In this paper, we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations, whose solutions have generally the initial singularity. To derive optimal order a posteriori error estimates, the quadratic reconstruction for the L1 method and the necessary fractional integral reconstruction for the first-step integration are introduced. By using these continuous, piecewise time reconstructions, the upper and lower error bounds depending only on … Show more

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