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A posteriori error analysis for discretisations of time-fractional subdiffusion problems

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FD2W01 - Deterministic and stochastic fractional diļ¬€erential equations and jump processes

We consider a subdiffusion problem where the fractional time derivative is approximated either by the L1 scheme or by convolution quadrature and derive a posteriori error estimates.  Our approach is based on appropriate pointwise representations of the numerical schemes as perturbed evolution equations and on stability estimates for the evolution equation. Extensive numerical experiments indicate the reliability and the optimality of the estimators for the schemes considered, as well as their efficiency as error indicators driving adaptive mesh selection locating singularities of the problem.   Joint work with: Charalambos G. Makridakis (IACM-FORTH Crete, University of Sussex)

This talk is part of the Isaac Newton Institute Seminar Series series.

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