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/
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.
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.
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)
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
- 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.
- MAGIC-098-AFEM 2020 boardshots (Omar Lakkis and Chandrasekhar Venkataraman, web)
- Finite elements: theory, fast solvers, and applications in elasticity theory (Dietrich Braess, book)
- A posteriori error estimation techniques for finite element methods (Rüdiger Verfürth, book)
- iFEM and adaptive finite element computational package in Matlab (R) (Long Chen, web)
- Convergence of adaptive finite element methods (Morin, P., R. Nochetto and K. Siebert , book)
- Adaptive finite element methods with convergence rates (Binev, Peter, Wolfgang Dahmen and Ron DeVore, book)
- Approximation and learning by greedy algorithms (Barron, Andrew R. et al. , arxiv)
- Quasi-optimal convergence rate for an adaptive fi- nite element method (Cascon, J. Manuel et al. , book)
- Axioms of Adaptivity (Carstensen, Carsten et al. , arxiv)
- Lecture Notes (in progress, file will change during term) (Omar Lakkis, web)
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
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
Only current consortium members and subscribers have access to these files.
Please log in to view course materials.
Lectures
Please log in to view lecture recordings.
