Literature: S. C. Brenner and L. R. Scott, 'The mathematical theory of finite element methods', 3rd ed., Springer, 2008.
The core of the course is the theory of finite elements in Chapters 3 and 4. In addition, we study some preparations from Chapters 0, 1, 2 and selected topics from Chapters 5-14.
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. As a by-product we also obtain a proof of Sobolev's inequality.
Depending on the available time and the interests of the participants we may also study some additional topics, such as, multigrid methods, maximum norm estimates, mixed methods.
Teacher: Stig Larsson
Schedule: to be decided at the first meeting.
First meeting: Monday January 16, 12.00-12.30. Room MV L14.
Lectures:
1.1 Introduction. Chapter 0. Weighted norm
estimates (notes).
1.2 Chapter 1.
Exercises:
/stig