Pointwise-in-time a posteriori error control for time-fractional parabolic equations

05/12/2021

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by   Natalia Kopteva, et al.

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For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L_2 and L_∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2-α in the presence of solution singularities.