Lecturer	Andy Wathen
Degrees	2009: Hilary Term — MSc in Mathematical Modelling and Scientific Computing
Term	Hilary Term 2009  (16 lectures)
Links	Also Part C of MMath degree

Overview

Computational algorithms are now widely used to predict and describe physical and other systems. Underlying such applications as Weather Forcasting, Civil Engineering (design of structures) and Medical Scanning are numerical methods which approximately solve partial differential equation problems. This course gives a mathematical introduction to one of the more widely used methods: the finite element method.

Prerequisites

No formal prerequisites are assumed. The course builds on elementary calculus, analysis and linear algebra and, of course, requires some aquaintance with partial differential equations such as the material covered in the Maths Mods Waves and Diffusion course, in particular the Divergence Theorem.

Part A Numerical Analysis would be helpful but is certainly not essential. Function Space material will be introduced in the course as needed.

Synopsis

Finite element methods represent a powerful and general class of techniques for the approximate solution of partial differential equations. The aim of this course is to introduce these methods for boundary value problems for the Poisson and related elliptic partial differential equations. Attention will be paid to formulation, analysis, implementation and applicability of these methods.

Syllabus

Elliptic boundary value problems in 1-dimension and 2-dimensions; variational and weak forms. Galerkin finite element methods; piecewise polynomials; implementation issues; a priori and a posteriori error analysis. Mixed finite element methods and the Stokes problem.

Reading list

The main text will be 

Howard Elman, David Silvester & Andy Wathen, Finite Elements and Fast Iterative Solvers,
Oxford University Press, 2005 [mainly Chapters 1 and 5]

and some of the introductory material is usefully covered in 

Endre Suli and David Mayers, An Introduction to Numerical Analysis, 
Cambridge University Press, 2003 [Chapter 11 and in particular Chapter 14]

and 

David Silvester, A Finite Element Primer, notes which can be found at 
http://www.maths.manchester.ac.uk/~djs/primer.pdf

Another book on finite elements which may be useful for different parts of the
course is

Claes Johnson, Numerical Solution of Partial Differential Equations by the 
Finite Element Method, Cambridge University Press, 1990. (which is unfortunately 
out of print) [Chapter 1-4]

and the Computing Lab lecture notes

Endre Suli, Finite Element Methods for Partial Differential Equations, 
Oxford University Computing Laboratory, 2001.

are also useful.

Taking our courses

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Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.