Lecture Computational PDEs II (SS 2025)
Theorie und Numerik partieller Differentialgleichungen II

Basic information

Lecture and exercises: Dietmar Gallistl
Friedolin info
Dates: see table below
Required preliminaries: basic knowledge on the finite element method^*; basic programming skills; basic linear functional analysis (Höhere Analysis I can be attendend in parallel)
(^* for example from one of the courses Iterative solvers for PDEs / Computational PDEs I / Numerical Analysis of instationary PDEs)
If you meet these requirements, you can follow the course without having attended Computational PDEs I.
This is a 6 ECTS course. We will meet roughly every second week (see schedule below) 8-12 for lectures and exercises. It is essential for the students to solve the theoretical problems and the programming assignments.
Oral exams on individual appointment.

Saddle-point problems; mixed finite elements; Stokes equations; linear elasticity; a posteriori error estimation

There are lecture notes: pdf file (regularly updated). The file also contains sections with problems and programming exercises.
Last update: 25-Apr-2025. (problem 2.7(b) will be discussed on 9-May)
Some software for getting started: LINK

See the bibliography in the lecture notes.

Problem solving: The table below displays the exercises to be discussed in the respective week (e.g., the exercises formulated in week 19 can be found in the row for week 20).
Legend:
orange=lecture

magenta=programming project (no class, individual appointments)

grey=no class (holiday)

Week	Friday	Exercises	Syllabus	References
15	11 Apr		BNB lemma, saddle-point problems	§2.1.1; Lemma 2.9
16	18 Apr
17	25 Apr	Problems 2.1--2.7	Brezzi splitting, Stokes equations	§2.1.3--2.2.1
18	02 May
19	09 May	Problems 2.8--2.12; Problems 1.22--1.23; Problem 2.17	Galerkin method, Mini element	§2.1.2,--2.1.3, §2.2.2
20	16 May
21	23 May
22	30 May
23	06 Jun
24	13 Jun
25	20 Jun
26	27 Jun
27	04 Jul
28	11 Jul