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.



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


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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