MAGIC098: Adaptive Finite Element Methods

Course details

Semester

Autumn 2017
Monday, October 9th to Friday, December 15th

Hours

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

Timetable

Mondays
11:05 - 11:55

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

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

  • Dr Omar Lakkis

    Dr Omar Lakkis

    University
    University of Sussex

Bibliography

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Assessment

The assessment for this course will be released on Monday 8th January 2018 and is due in by Monday 22nd January 2018 at 23:59.

The assessment for this course will consist in a student-selected answers to a list of of 10 to 20 questions.
These will be collected as we go through the course and often given in the form of ëxercises" or "problems" during the lectures.
A digest of these questions, road-fitted for the final assessment, along with a rough-version of the lecture notes, will be uploaded here towards the end of the course (so a good idea to prepare for the assessment is to go through all the exercises and gaps in the lecture notes).
The criterion for choosing the exercises, besides the student's own taste, will be a total of 100 marks, based on questions associated with each of the questions (easier questions will have less marks, as an incentive to work on the harder ones).

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

Files

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Lectures

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