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MA50170: Numerical solution of PDEs I

Follow this link for further information on academic years Academic Year: 2013/4
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 2
Further information on unit assessment Assessment: CW 40%, EX 60%
Further information on supplementary assessment Supplementary Assessment: MA50170 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites:
Further information on descriptions 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. They should be able to demonstrate an in-depth understanding of the subject.

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. Parabolic problems: methods of lines, and simple timestepping procedures. Stability and convergence.
Further information on programme availabilityProgramme availability:

MA50170 is Optional on the following programmes:

Department of Mathematical Sciences
  • TSMA-AFM09 : MSc Mathematical Sciences (Full-time)
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time)
  • TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time)
  • TSMA-AWM14 : MSc Modern Applications of Mathematics (Full-time incorporating placement)
  • TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time)

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.