BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kris van der Zee (University of Nottingham) DTSTART:20210223T070000Z DTEND:20210223T080000Z DTSTAMP:20260423T035627Z UID:CMWebinar/2 DESCRIPTION:Title: Minimal Residual Finite Element Methods in Banach Spaces\nby Kris va n der Zee (University of Nottingham) as part of Australian Seminar on Comp utational Mathematics\n\n\nAbstract\nMinimal-residual (MinRes) finite elem ent methods have attracted significant attention in the recent numerical a nalysis literature\, owing to their conceptual simplicity and striking sta bility properties. While these methods include classical least-squares and optimal Petrov-Galerkin methods\, recent advances centre around the minim isation of residuals measured in a (discrete) dual norm\, such as the disc ontinuous Petrov--Galerkin (DPG) methodology. \n\nIn this talk\, I will fi rst discuss how MinRes methods can be extended to Banach-space settings. T his general setting allows for a direct discretization of PDEs in nonstand ard non-Hilbert settings that are required when facing rough data and low- regular solutions. This development gives rise to a class of nonlinear Pet rov--Galerkin methods\, or\, equivalently\, abstract mixed methods with mo notone nonlinearity. Discrete stability and quasi-optimal convergence foll ow under a Fortin condition. I will consider applications to PDEs (linear transport\, advection-diffusion)\, as well as the regularization of rough linear functionals. \n\nSecondly\, I will show how the MinRes framework ca n be utilised for model reduction. In particular\, I will present a machin e-learning framework to train a provably stable parametric Petrov-Galerkin method on a fixed underlying mesh\, whose aim is to ensure highly accurat e quantities of interest regardless of the mesh size. Some recent numerics will illustrate these ideas.\n LOCATION:https://researchseminars.org/talk/CMWebinar/2/ END:VEVENT END:VCALENDAR