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General


Description

The main prerequisite is a strong motivation to undertake research related in modern aspects functional approximation theory, data compression, related algorithms, or the numerical analysis of partial differential equations.
A solid background in undergraduate analysis and partial differential equations, some basic functional or harmonic analysis, or numerical analysis will be useful.

Semester

Autumn 2017 (Monday, October 9 to Friday, December 15)

Timetable

  • Mon 11:05 - 11:55

Prerequisites

No prerequisites information is available yet.

Syllabus

We start by reviewing the standard Galerkin method with a focus on numerical approximation methods such as wavelet Galekrin, finite elements and discontinuous Galerkin for elliptic and parabolic equations, including the needed element of functional analysis, e.g., Sobolev and Besov spaces. We then recall the apriori error analysis of such methods and move onto aposteriori error analysis. We follow up this with an overview of the literature on adaptive methods and their convergence analysis with a focus on complexity of algorithms. Time allowing we look at connections between wavelet and Galerkin methods or space-time methods for parabolic (perhaps hyperbolic) problems. (NB to be reduced to 10 hours)

Lecturer


Omar Lakkis
Email O.Lakkis@sussex.ac.uk
Phone
Photo of Omar Lakkis


Students


Photo of Puneet Matharu
Puneet Matharu
(Manchester)
Photo of Rawin Youngnoi
Rawin Youngnoi
(Birmingham)


Bibliography


Adaptive finite element methods with convergence ratesBinev, Peter, Wolfgang Dahmen and Ron DeVore
Approximation and learning by greedy algorithmsBarron, Andrew R. et al.
Axioms of AdaptivityCarstensen, Carsten et al.
Quasi-optimal convergence rate for an adaptive fi- nite element methodCascon, J. Manuel et al.
Convergence of adaptive finite element methodsMorin, P., R. Nochetto and K. Siebert


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Assessment



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Recorded Lectures


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