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401-3651-00L 10 Credits

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Numerical methods for elliptic and parabolic partial differential equations

Numerik partieller Differentialgleichungen

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 15:00:00

Abstract

The course gives a comprehensive introduction into the numerical treatment oflinear and non-linear elliptic boundary value problems and related eigenvalueproblems and parabolic evolution problems. Emphasis is on theory and thefoundations of numerical methods. Practical exercises involve MATLAB implementationof 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 * Finite difference and finite volume methods * 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

P. Knabner and L. Angermann: Numerical Methods for Elliptic and Parabolic Partial Differential Equations Ch. Grossmann and H.-G. Roos: Numerik partieller Differentialgleichungen D. Braess: Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. S. Sauter and C. Schwab: Randelementmethoden S. Brenner and R. Scott: Mathematical theory of finite element methods

General Information

Language: English (lecture), German (exercise)
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 08:15-10:00 (HG G 3) Thu 08:15-10:00 (HG G 3)	4 h weekly
exercise	Numerical methods for elliptic and parabolic partial differential equations	Thu 10:15-11:00 (HG E 5)	1 h weekly