In this seminar, we discuss solvability and numerical approximation of time-dependent partial-differential equations, including the heat and wave equation. In particular, we investigate the appropriate function spaces for the analysis of the problems, and we study the proof of existence and uniqueness by means of Galerkin approximation and the Rothe method. These two methods are based on discretization in space and time, respectively, so they also provide a first step towards the numerical solution. The basic arguments are introduced for the linear heat and wave equation. We also investigate how they can be generalized to more complicated examples, including nonlinear equations and evolution problems of mixed (parabolic/elliptic/hyperbolic) type.
| Date | Time | Room | Speaker | Title |
|---|---|---|---|---|
| Tue, 2025-03-04 | 14:30 – 15:15 | S2 059 | Preliminary Discussion | |
| Tue, 2025-03-11 | No seminar | |||
| Tue, 2025-03-18 | 13:45 – 15:15 | S2 059 | Andreas Schafelner | Bochner Spaces (Evans Chapter 5, Schweizer, Kap. 10) |
| Tue, 2025-03-25 | 13:45 – 15:15 | S2 059 | Christoph Dormayr | Galerkin Method for Parabolic Problems (Evans Chapter 7.1) |
| Tue, 2025-04-01 | 13:45 – 15:15 | S2 059 | Alessio Cesarano | Rothe method (Wu Chapter 3.2, Schweizer Kap. 11) |
| Tue, 2025-04-08 | 13:45 – 15:15 | S2 059 | Felix Engertsberger | Wave equation (Evans Chapter 7.2, Schweizer, Kap. 12) |
| Tue, 2025-04-15 | Easter Break | |||
| Tue, 2025-04-22 | Easter Break | |||
| Tue, 2025-04-29 | 13:45 – 15:15 | S2 059 | Marvin Fritz | Nonlinear equations |
| Tue, 2025-05-06 | 13:45 – 15:15 | S2 059 | Nepomuk Krenn | Magnetoquasistatics |
| Tue, 2025-05-13 | 13:45 – 15:15 | S2 059 | Eva-Maria Haslhofer | Application to electrical machines |
| Tue, 2025-05-20 | 13:45 – 15:15 | S2 059 | Felix Dressler | Thermoelasticity |
| Tue, 2025-05-27 | 13:45 – 15:15 | S2 059 | Paula Kohlberger | Poroelasticity |
| Tue, 2025-06-03 | 13:45 – 15:15 | S2 059 | Martin Datzberger | Viscoelasticity |
| Tue, 2025-06-10 | Pentecost Break | |||
| Tue, 2025-06-17 | No seminar | |||
| Tue, 2025-06-24 | No seminar |