The mathematical description of many physical phenomena naturally leads to nonlinear partial differential equations. While, in some cases, these are commonly approximated by linear equations (e.g., heat flow), this is often not possible, because the structure of the problem is far from being linear.
In this lecture we will consider various aspects of nonlinear partial differential equations. On the one hand we will discuss mathematical modelling and analytical questions. On the other hand we will introduce basic numerical methods for such problems, ranging from discretization to efficient iterative methods.
The problems considered will, e.g., cover applications from material science (phase field models), and bio-mechanics.
Advanced students in the Master Program Mathematics and of BMS. Various possible topics for a Master thesis will come up during this course.
Basic knowledge on partial differential equations and their numerical solution (e.g. Numerics III).
For more information please see the lecture homepage
- D. Braess: Finite Elemente. Springer, 3rd edition (2000)
- P. Knabner, L. Angermann: Numerik partieller Differentialgleichungen. Springer (2000)
- P. Deuflhard, M. Weiser: Numerische Mathematik 3. De Gruyter (2011)
- J. Wloka: Partielle Differentialgleichungen. Teubner (1982)
- D. Werner: Funktionalanalysis. Springer, Berlin (2000)