A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations

02/27/2022

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by   Natalia Kopteva, et al.

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An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form ∑_i=1^ℓq_i(t) D _t ^α_i u(x,t), where the q_i are continuous functions, each D _t ^α_i is a Caputo derivative, and the α_i lie in (0,1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in L_2(Ω) and L_∞(Ω), where the spatial domain Ω lies in ^d with d∈{1,2,3}. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm.