Optimal discretisation in Banach spaces

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• Dr Kris van der Zee, University of Nottingham
• Monday 28 November 2016, 15:00-16:00
• Arts Lecture Room 1.

If you have a question about this talk, please contact David Smith.

Is it possible to obtain near-best approximations to solutions of linear operator equations in a general Banach space setting? Can this be done with guaranteed stability?

In this seminar, I address these questions by considering nonstandard, nonlinear, Petrov-Galerkin discretizations. These methods are particularly useful for PDEs with rough data or nonsmooth solutions having discontinuities.

I build on ideas of residual minimization and the recent theory of optimal Petrov-Galerkin methods in Hilbert-space settings. I will demonstrate that the implementable version of the Petrov-Galerkin formulation is naturally related to a mixed method with a monotone nonlinearity. In the setting of certain special Banach spaces, I will prove optimal a priori error estimates (a la Cea / Babuska), with constants depending on the geometry of the involved Banach spaces.

This is joint work with Ignacio Muga of Pontificia Universidad Catolica de Valparaiso.

This talk is part of the Applied Mathematics Seminar Series series.

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• Applied Mathematics Seminar Series
• Arts Lecture Room 1
• School of Mathematics events

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