Advanced Numerical Methods

10 credits

Syllabus, Master's level, 1TD050

A revised version of the syllabus is available.
Education cycle
Second cycle
Main field(s) of study and in-depth level
Computational Science A1F, Computer Science A1F, Technology A1F
Grading system
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 10 March 2016
Responsible department
Department of Information Technology

Entry requirements

120 credits in science/engineering including 45 credits in mathematics, where linear algebra, vector calculus, transform theory (Fourier analysis) must be covered. Scientific Computing III. Applied Finite Element Methods or Finite Element Methods.

Learning outcomes

To pass the course the student shall be able to

  • review and apply fundamental theory for mathematical modelling of partial differential equations;
  • analyse finite difference and finite element approximations of systems of partial differential equations;
  • review and describe application areas where different types of finite element and finite differences are used;
  • choose, formulate and implement appropriate numerical methods for solving science and engineering problems that are formulated as partial differential equations;
  • interpret, analyse and evaluate results from numerical computations;
  • use common software to solve application problems formulated as more complicated partial differential equations, such as linear elasticity and transport problems.


The content is built up around a design problem. It focuses on keywords such as consistency, convergence, stability, existence, uniqueness and efficiency.

The course covers the Fourier method, Energy method, normed vector spaces, bilinear forms, Lp - and Sobolev spaces, weak derivatives, elliptic boundary value problems, hyperbolic and parabolic time-dependent initial value problems, linearisation for nonlinear problems, interpolants and finite elements, higher order methods and elements, stabilisation, a priori and posteriori error bounds.

Analyse linear systems of partial differential equations, analyse finite difference and finite element methods of systems of nonlinear partial differential equations. The methodology in finite difference and finite element methods (Lax-Richtmeyer, Lax-Milgram) and applying explicit and implicit time discretisation methods.


Lectures, problem solving sessions and assignments.


Written final exam (6 credits) and assignments (4 credits).