MAGIC098: Adaptive Finite Element Methods

Course details

A specialist MAGIC course

Semester

Autumn 2022
Monday, October 3rd to Friday, December 9th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

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. 

Prerequisites

Requirements are standard year 3 or master's level Analysis and some knowledge of elliptic partial differential equations.

Exposure to Galerkin or finite element methods (as taught in spring term MAGIC100 or equivalent) will be helpful though not essential. "Review" material will be uploaded. 

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

  • Kv

    Dr Kris van der Zee

    University
    University of Nottingham

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Monday 9th January 2023 and is due in by Saturday 21st January 2023 at 23:59.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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