johanna.mcbryde@icms.org.uk      0131 650 9816

What is Numerical Analysis?

This course is run by MIGSAA. It is open to everyone, including non-MIGSAA students, as an SMSTC supplementary module.

ALL FURTHER INFORMATION ABOUT THIS COURSE WILL BE POSTED AT http://www.macs.hw.ac.uk/~hg94/na18.

 

Format: 10 lectures of 2 hours each, additional student lectures.

A similar course "What is ... PDEs?" currently runs informally at HW. The format is highly interactive, where students and upcoming seminar talks determine the content of the lectures.


Credits: 15 for students giving a lecture, less for participation or active contribution to tutorials


Aim: This course aims to give an introduction to standard techniques in the numerical analysis of partial differential equations, with a focus on the underlying analysis.


Prerequisites: a previous course in either PDE or their numerical analysis


Contents:

We cover some essential basic and advanced topics in the numerical analysis of PDEs. After the course the student should know key ideas in a broad range of topics, as they are relevant in their research or in relevant numerical analysis talks.

In particular, we expect to touch on the following topics:

  • Basics I: Numerical methods, such as finite differences, finite elements, finite volume methods, boundary elements, time-stepping schemes
  • Basics II: Relevant topics in analysis, such as approximation properties of functions, Sobolev spaces and functional analysis
  • Finite element methods for elliptic problems: Conforming variational and mixed methods, error analysis, adaptive methods
  • Non-conforming and non-standard methods
  • Finite elements for the Stokes problem, analysis and stabilisation
  • Heat and wave equations: time-stepping schemes and their analysis
  • Fast solvers: review of numerical linear algebra, preconditioning, multigrid methods
  • Applications in computational mechanics, fluid dynamics or biology

Some references:

  • D. Braess, Finite elements: Theory, fast solvers, and applications in solid mechanics, Cambridge University Press
  • H. Gimperlein, Interface and contact problems, lecture notes
  • Y. Saad, Iterative methods for sparse linear systems, SIAM
  • E.P. Stephan, Theory of approximation methods, lecture notes


Student talks:

Interested students will give a 60-minute lecture on a topic of their choice, ideally a topic related to their research interests.

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Tel : 0131 650 9816

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Mail : johanna.mcbryde@icms.org.uk