Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations. (English) Zbl 1514.65116
Summary: Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [N. Kopteva, Appl. Math. Lett. 123, Article ID 107515, 8 p. (2022; Zbl 1524.65560); N. Kopteva and M. Stynes, J. Sci. Comput. 92, No. 2, Paper No. 73, 23 p. (2022; Zbl 1492.65240)]. We improve the earlier time stepping algorithm based on this theory, and specifically address its stable and efficient implementation in the context of high-order methods. The considered methods include an L1-2 method and continuous collocation methods of arbitrary order, for which adaptive temporal meshes are shown to yield optimal convergence rates in the presence of solution singularities.
MSC:
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
time-fractional; subdiffusion; a posteriori error estimation; adaptive time stepping algorithm; higher-order methods; stable implementationReferences:
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