Numerical Solution of Evolutionary Equations (NMNV536) (Summer Semester 2020/2021)
This lecture course will cover the various theoretical and practical aspects of the numerical solution of evolution differential equations. Topics covered will include:
- Rothe method for parabolic problems. Existence and regularity of solutions, discretization error of the Rothe method.
- Higher order discretizations of time derivatives, discontinuous Galerkin method in time. Discretization of hyperbolic problems.
- Nonstationary advection and convection problems: Gibbs phenomenon, stabilization by artificial diffusion, semi-Lagrangian methods.
- Evolutionary problems on time-dependent domains: ALE method, level set methods.
Exams:
The final exam will consist of a 30 minute oral examination on the topics covered.
You can register for the examination in SIS - currently the following dates are available:
- Friday 11.06.21 — 13:00–16:00
- Thursday 24.06.21 — 11:00–12:30 & 13:30–15:00
Further dates in July and September will be added later if necessary.
Preferably the exam will be in-person in my office (K462, 4th floor in Karlin). In order to take the exam you will need to meet the current COVID guidelines from MFF for building entry. Copy of the necessary proof will need submitting during the exam.
If you prefer to take the exam online via Zoom please email me directly.
Lectures:
- Wednesday 17:20 – 18:50, Online via Zoom (Recordings/Notes)
Due to the current Covid-19 restrictions the teaching will be online only via Zoom. Details on how to connect to the Zoom meeting will be emailled directly to all registered users (using the email address registered in SIS). If you have not received this email please contact me directly at congreve[at]karlin.mff.cuni.cz.
Suggested Reading:
- K. Rektorys. Metoda časové diskretizace a parciální diferenciální rovnice, Teoretická knižnice inženýra, SNTL, Praha 1985
- V. Thomée, Galerkin finite element methods for parabolic problems, vol. 25, Springer-Verlag, Berlin Heidelberg, 2006.
- W. Hundsdorfer and J. G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Comput. Math. 33, Springer, 2003