Lecture "Numerical Methods for Singularly Perturbed Differential Equations" (WS 2024/2025)

Jun.-Prof. Dr. Mira Schedensack
Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut


Participants:

The lecture is suitable for students in mathematics (Diplom Mathematik and Diplom Wirtschaftsmathematik) and in mathematical physics with the standard knowledge from the introductory lectures and from functional analysis. It is possible to attend the lecture functional analysis in parallel. Basic knowledge in computational partial differential equations is helpful, but not necessary.

Content:

Singularly perturbed problems are differential equations in which the highest derivative appears with a small parameter ε in front. If ε tends to zero, the differential equation changes its character. For small values of ε, the solution exhibits boundary layers and standard numerical methods fail in the approximation. This lecture will mainly focus on the singularly perturbed differential equation

-ε Δ u + b · ∇ u = f

and it will discuss several methods for the numerical approximation of the solution including finite difference methods and finite element methods with upwind, and layer-adapted meshes.

Time of lectures

From 21 October onwards we will start at 9:00.

The lecture will take place on monday from 09:00-10:45 in A314 and from 11:00-12:15 in SG 3-14. The second lecture will contain also implementational aspects, exercises, and interactive elements.

News

The first lecture will take place on monday, October 14 at 9:15.

Material

The lecture is mainly based on the book "Robust Numerical Methods for Singularly Perturbed Differential Equations" by H.-G. Roos, M. Stynes, and L. Tobiska.
Code
Finite Differenzen in 1d (Version vom 11.11.2024)

FD2.m (Version vom 10.01.2025)

computeFDsolution.m (Version vom 10.01.2025)