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DTSTART:20200308T070000
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DTSTART;TZID=America/New_York:20201020T150000
DTEND;TZID=America/New_York:20201020T160000
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SUMMARY:Abner J. Salgado\, University of Tennessee\, Knoxville\, Fractional Gradient Flows
DESCRIPTION: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\nevolution 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. \nWe 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. \nWe provide an a priori error estimate that seems optimal in light of the regularizing effects proved above. We also develop an a posteriori\nerror estimate\, in the spirit of [Nochetto\, Savare\, Verdi\, CPAM 2000] and show its reliability. \nThis is ongoing work with Wenbo Li (UTK). \n \nOrganizer: A. Saibaba
URL:https://math.sciences.ncsu.edu/event/abner-j-salgado-university-of-tennessee-knoxville-fractional-gradient-flows/
LOCATION:Zoom
CATEGORIES:Numerical Analysis Seminar
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