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.

Syllabus/topics

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

Lecture notes and software

• There are lecture notes: pdf file (regularly updated). The file also contains sections with problems and programming exercises.
  Last update: 7-July-2025
• Some software for getting started: LINK

Literature

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, quasi-interpolation	§2.1.2--2.1.3, §1.1.3
  20	16 May	Problems 1.35, 1.36, 1.40, 1.41, 1.44, 1.47	quasi-interpolation, Mini element	§1.1.3, §2.2.2--2.2.3
  21	23 May
  22	30 May
  23	06 Jun	Problems 1.43, 1.46, 1.48, 1.49; Problems 2.13--2.15; Problem 2.18	duality, mixed Laplacian, H(div) and its traces	§2.3.1--2.3.2
  24	13 Jun	Problems 2.19--2.25	Raviart-Thomas element	§2.3.3
  25	20 Jun	Problems 2.25--2.27, 2.31--2.34	details on traces and H1/2 spaces	§3.1
  26	27 Jun	Problem 2.28
  27	04 Jul	Problem 2.28, Problems 3.1--3.6, Lemma 3.11	linear elasticity, locking	§4.1
  28	11 Jul	Problems 4.1--4.4	hypercircle, a posteriori error estimates	§2.3.6