401-3651-00L  Numerical Methods for Elliptic and Parabolic Partial Differential Equations

SemesterAutumn Semester 2013
LecturersP. Grohs
Periodicityyearly recurring course
Language of instructionEnglish
CommentCourse audience: 3rd year ETH BSc Mathematics and MSc Mathematics and MSc Applied Mathematics students.
Other students are advised to attend the course "Numerical Methods for Partial Differential Equations" (401-0674-00L) in the CSE curriculum during the spring semester.


AbstractThis course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises include MATLAB implementations of finite element methods.
ObjectiveParticipants of the course should become familiar with
* concepts underlying the discretization of elliptic and parabolic boundary value problems
* analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems
* methods for the efficient solution of discrete boundary value problems
* implementational aspects of the finite element method
ContentA selection of the following topics will be covered:

* Elliptic boundary value problems
* Galerkin discretization of linear variational problems
* The primal finite element method
* Mixed finite element methods
* Discontinuous Galerkin Methods
* Boundary element methods
* Spectral methods
* Adaptive finite element schemes
* Singularly perturbed problems
* Sparse grids
* Galerkin discretization of elliptic eigenproblems
* Non-linear elliptic boundary value problems
* Discretization of parabolic initial boundary value problems
Lecture notesCourse slides will be made available to the audience.
LiteratureD. Braess: Finite Elements, THIRD Ed., Cambridge Univ. Press, (2007).
(Also available in German.)
V. Thomee: Galerkin Finite Element Methods for Parabolic Problems,
SECOND Ed., Springer Verlag (2006).

Additional Literature:
D. A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, vol. 69 SMAI Mathématiques et Applications,
Springer, 2012 [DOI: 10.1007/978-3-642-22980-0]
Ch. Grossmann and H.-G. Roos: Numerik partieller Differentialgleichungen.
S. Brenner and R. Scott: Mathematical theory of finite element methods.
Prerequisites / NoticePractical exercises based on MATLAB