Thackeray Hall 704

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https://pitt.zoom.us/j/99400392432

Meeting ID: 994 0039 2432

Passcode: 032779

### Abstract or Additional Information

We consider a so-called fractional gradient flow: an

evolution equation aimed at the minimization of a convex and l.s.c.

energy, but where the evolution has memory effects. This memory is

characterized by the fact that the negative of the (sub)gradient of the

energy equals the so-called Caputo derivative of the state.

We introduce a notion of "energy solutions" for which we refine the

proofs of existence, uniqueness, and certain regularizing effects

provided in [Li and Liu, SINUM 2019]. This is done by generalizing, to

non-uniform time steps the "deconvolution" schemes of [Li and Liu,

SINUM 2019], and developing a sort of "fractional minimizing movements"

scheme.

We provide an a priori error estimate that seems optimal in light of

the regularizing effects proved above. We also develop an a posteriori

error estimate, in the spirit of [Nochetto, Savare, Verdi, CPAM 2000]

and show its reliability.

This is joint work with Wenbo Li (UTK).