Credits:
 6 
Level:
 Honours (FHEQ level 6) 
Period: 
Semester 2

Assessment:
 CW 25%, EX 75% 
Supplementary Assessment:  MA30170 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:
 Before taking this unit you must take MA20218 and take MA20219 and take MA20222 
Description:
 Aims & Learning Objectives:
Aims: To teach numerical methods for elliptic and parabolic partial differential equations via the finite element method based on variational principles.
Objectives:
At the end of the course students should be able to derive and implement the finite element method for a range of standard elliptic and parabolic partial differential equations in one and several space dimensions. They should also be able to derive and use elementary error estimates for these methods.
Content:
* Introduction.
* Variational and weak form of elliptic PDEs. Natural, essential and mixed boundary conditions. Linear and quadratic finite element approximation in one and several space dimensions. An introduction to convergence theory.
* System assembly and solution, isoparametric mapping, quadrature, adaptivity.
* Applications to PDEs arising in applications.
* Brief introduction to time dependent problems.

Programme availability:

MA30170 is Optional on the following programmes:
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 3
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM09 : MSc Mathematical Sciences (Fulltime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 2
 TSMAAFM08 : MSc Modern Applications of Mathematics (Fulltime)  Year 1
 TSMAAFL02 : PG Dip Modern Applications of Mathematics (Fulltime)  Year 1
