NUMN33 Numerical Methods for Partial Differential Equations, 7.5 credits, is an elective course for second-cycle studies for a degree of Master of Science in Mathematics with specialisation in Numerical Analysis, and an elective course for second-cycle studies for a degree of Master of Science in Computational Science. The course is given in English.

LTH-course code: FMNN45

Third-cycle (doctoral) course code: FMNN45F

Course Content

The course gives an introduction to error estimates, convergence and stability, as well as existence and regularity of solutions to elliptic differential equations (PDEs). This is followed by an introduction to DUNE-FEM which discusses how elliptic PDEs can be
discretized using the Finite Element Method (FEM). In particular it considers:

Weak theory for elliptic PDEs: existence and error estimates,
Construction of Finite Elements, e.g. discretization grids, reference elements
degree-of-freedom (DOF) mappings,
Unified Form Language (UFL) for description of weak forms of partial differential equations
Parallelization of Finite Element methods using domain decomposition, and
Adaptive Finite Elements.

Teaching
The teaching consists of lectures. A number of compulsory projects carried out in small groups are included in the course. Attendance at all oral group presentations of the project results is mandatory. Independent problem solving using computers is a central part of the course.

Assessment
The examination consists of a written final report and an appurtenant oral presentation of the projects at the end of the course.

Course Literature

Larsson, Stig & Thomée, Vidar. (2009). Partial differential equations with numerical methods. Springer. ISBN: 9783540887058
Renardy, Michael & Rogers, Robert C.. (1993). An introduction to partial differential equations. Berlin : Springer-Vlg. ISBN: 0387979522 & 3540979522
Brenner, Susanne C. & Scott, L. Ridgway. (1994). The mathematical theory of finite element methods. Springer. ISBN: 3540941932 & 0387941932
Ciarlet, Philippe G.. (1978). The finite element method for elliptic problems. North-Holland. ISBN: 0-444-85028-7
Thomée, Vidar. (2006). Galerkin finite element methods for parabolic problems. Springer. ISBN: 3540331212 & 9783540331216

Official Course Description

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Numerical Analysis at Faculty of Science