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MA50170: Numerical solution of elliptic PDEs

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
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 Summary: CW 40%, EX-TH 60%*
Further information on unit assessment Assessment Detail:
  • Class Test* (CW 8%)
  • Coursework 1* (CW 7%)
  • Coursework 2* (CW 25%)
  • Open Book Examination with a Duration of 24 hours* (EX-TH 60%)

*Assessment updated due to Covid-19 disruptions
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: In taking this module you cannot take MA30170 . Before taking this unit you must take MA20222 or an equivalent first course in numerical analysis.
Further information on descriptions Description: Aims:
To teach the finite element method for elliptic PDEs based on variational principles.

Learning Outcomes:
At the end of the course, students should be able to derive and implement the finite element method for a range of elliptic PDEs in one and several space dimensions, including problems with random coefficients. 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.

Skills:
Understanding of the finite element method (T, A), Computer programming with the finite element method (T, A).

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. PDEs with random coefficients. Examples of intrusive and non-intrusive methods (e.g., Monte Carlo methods and stochastic Galerkin methods).
Further information on programme availabilityProgramme availability:

MA50170 is Optional on the following programmes:

Department of Mathematical Sciences

Notes: