MAGIC098: Adaptive Finite Element Methods

Course details

A specialist MAGIC course

Semester

Autumn 2020
Monday, October 5th to Friday, December 11th

Hours

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

Timetable

Wednesdays
10:05 - 10:55 (UK)

Announcements

Course material is found (and constantly updated) on this online repository:

https://www.maths.sussex.ac.uk/Staff/OL/Pickup/Sokrates/MAGIC-098-AFEM/2020/

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) 

Lecturers

  • Dr Omar Lakkis

    Dr Omar Lakkis

    University
    University of Sussex
    Role
    Main contact
  • CV

    Dr Chandrasekhar Venkataraman

    University
    University of Sussex

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Assessment

The assessment for this course will be released on Monday 11th January 2021 at 00:00 and is due in before Wednesday 27th January 2021 at 23:59.

Assessment is due in January (rely on MAGIC admin for precise dates) and appears here over the winter break. It consists of one long question with a menu including analysis and computations, which can be self-tailored by the student.

A freshly updated copy of the assessment question is permanently available here: https://www.maths.sussex.ac.uk/Staff/OL/Pickup/Sokrates/MAGIC-098-AFEM/2020/MAGIC098-2021-final-assessment-questions.pdf

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

Files

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Lectures

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