Finite Element Methods

Third-cycle level | 7.5 credits | Course code: NFMV009
VT 2020
Study period: 2020-01-20 - 2020-03-28
LANGUAGE OF INSTRUCTION: The course is given in English
Application period: 2019-10-11 - 2020-01-05

Course description

In this course we first study how to construct finite element function spaces based on triangular or rectangular element domains and piecewise polynomials. Then we develop the associated approximation theory based on averaged Taylor polynomials and Riesz potentials. This leads to interpolation error estimates in Sobolev norms. We then consider convergence of adaptive schemes. In the second part of the course we focus on applications of the theoretical framework to other equations.

The first part of the course is based on Chapters 0-4 and 9 in The Mathematicla Theory of Finite Element Methods, by Brenner & Scott, with emphasis on Chapters 3 and 4. In the second part we will consider selected topics from the remaining chapters as well as other material. In the second part, the participants will take an active role in selecting and presenting the material.

The course covers important results from the theory of Sobolev spaces, variational formulation of elliptic boundary value problems and the formulation of the finite element method, construction of finite elements, polynomial approximation theory in Sobolev spaces, convergence of adaptive algorithms as well as applications of the theoretical results to other equations.

Requirements and Selection

Entry requirements

Some experience with partial differential equations,, finite element methods, functional analysis and Sobolev spaces, corresponding to, e.g., Chapter 5 of S. Larsson and V. Thomee, Partial Differential Equations with Numerical Methods, Texts in Applied Mathematics 45, Springer (2003).


Not relevant

Course syllabus


Reading and reference list

Reading and reference list for the course


Department of Mathematical Sciences


Natural Science and Mathematics


finite, element, method, numerical, analysis

CONTACTAxel Målqvist