Numerical Analysis: Numerical Methods for Partial Differential Equations
Learn how to simulate complex physical systems using advanced numerical methods. This course explores how partial differential equations are solved with modern tools such as the Finite Element Method and software packages like DUNEFEM.
Start
Spring 2027
Level
Master's
Language
English
Place of study
Lund
Course code
NUMN33
This course deepens your understanding of numerical methods for partial differential equations (PDEs), with a focus on elliptic problems. You will learn how to analyze, discretize, and solve PDEs using the Finite Element Method (FEM) and the DUNE-FEM software framework. The course combines theory with hands-on work on realistic computational problems.
Topics covered include
- Weak theory for elliptic PDEs: existence and error estimates
- Construction of finite elements: grids, reference elements, DOF mappings
- Unified Form Language (UFL) for describing weak formulations
- Parallelization using domain decomposition
- Adaptive Ffinite Eelement Mmethods.
NUMN33 is an alternativecompulsory advancedlevel course within the Master’s Programme in Mathematics with a specialization in Numerical Analysis, and an elective within the Master’s Programme in Computational Science at Lund University. Bachelor’s students in mathematics may take the course as an optional part of their programme. It is also available as a standalone course.
The course combines lectures with practical group projects. You will work in small teams to solve problems and present your results both in writing and orally. All group presentations are mandatory and form part of the final assessment.
Expect a hands-on learning experience where theory meets practice. You will implement numerical methods, explore solution strategies, and use DUNE-FEM to run simulations. The final examination consists of a written report and an oral presentation.
This course prepares you for advanced work in numerical analysis, computational science, and applied mathematics. You will gain skills that are valuable in research, industry, and further academic studies. The ability to model and solve PDEs is essential in fields such as engineering, physics, climate modelling, and finance. After completing the course, you will be equipped to tackle complex simulation tasks and contribute to scientific and technological development.
Entry requirements
Admission to the course requires English 6/b and at least 90 credits in natural sciences or engineering, of which at least 45 credits should be in mathematics and/or numerical analysis, including knowledge corresponding to the courses NUMA01 Computational Programming with Python, 7.5 credits, and NUMN32 Numerical Methods for Differential Equations, 7.5 credits.
Selection criteria
Seats are allocated according to: ECTS (HPAV): 100 %.
Tuition fees for non-EU/EEA citizens
Citizens of countries outside:
- The European Union (EU)
- The European Economic Area (EEA) and
- Switzerland
are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.
Tuition fees, payments and exemptions
Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125
Note that you may also need to pay an application fee, or provide proof of exemption.
No tuition fees for citizens of the EU, EEA and Switzerland
There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.
A shared second home for mathematics
Matematikcentrum gathers students and researchers in mathematics, mathematical statistics, and numerical analysis and computational science. Along Sölvegatan, close to green spaces and the wider university area, you find a shared environment for everyone who uses mathematics as a common language. Research here has led to innovations and companies in areas such as optimisation, image analysis and software, with applications ranging from logistics to video analysis and mobile technology.
