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401-3651-00L 10 Credits BSC , MSC D-MATH
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Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Lecturers & Examiners: Prof. Dr. Ralf Hiptmair
This course is meant for bachelor and master students of mathematics. Students of physics and computer science are advised to attend the parallel course "Numerik der Differentialgleichungen" in the CSE curriculum.
VVZ CR n/a

Last Updated: 2026-02-05 15:23:57

Abstract

The course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems and related eigenvalue problems and parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises involve MATLAB implementation of finite element methods.

Objective

Participants 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

Content

* 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

Resources

Lecture Notes

Course slides will be made available to the audience.

Literature

D. Braess: Finite Elements, DRITTE Auflage, Cambridge Univ. Press, (2007). V. Thomee: Galerkin Finite Element Methods for Parabolic Problems, SECOND Ed., Springer Verlag (2006). additional literature: P. Knabner and L. Angermann: Numerical Methods for Elliptic and Parabolic Partial Differential Equations. Ch. Grossmann and H.-G. Roos: Numerik partieller Differentialgleichungen. S. Sauter and Ch. Schwab: Randelementmethoden. S. Brenner and R. Scott: Mathematical theory of finite element methods.

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Numerical Methods for Elliptic and Parabolic Partial Differential Equations
  • Tue 15:15-17:00 (HG E 5)
  • Thu 10:15-12:00 (HG E 5)
  • Thu 13:15-15:00 (HG E 5)
4 h weekly
exercise Numerical Methods for Elliptic and Parabolic Partial Differential Equations
  • Thu 10:15-11:00 (HG F 26.5)
1 h weekly

Offered In