# Graduate seminar WS 23/24 Graduate Seminar on Numerical Analysis

## Space-time methods

Dates will be fixed in the preliminary meeting beginning October depending on availability of the students.

Time-dependent partial differential equations (PDEs) are typical models for many scientific and engineering applications. The standard approach for the numerical solution of such problems are time-stepping methods, which either discretize first in space and then in time or vice versa. Concerning adaptive refinement, these suffer from the fact that the time increment is independent of the spatial location. However, since the PDE solution can have singularities in space and time, flexible adaptive refinement is mandatory to regain optimal convergence rates of the error with respect to the computational cost. Another major drawback of time-stepping methods is that they are inherently sequential in time, and therefore not well suited for parallelization.

Due to the rapid development of parallel computers, space-time methods, which aim to solve the problem as a whole and treat time as yet another dimension, have become a promising alternative. Indeed, the space-time approach has none of the aforementioned shortcomings. It has the potential to construct meshes that are optimally adapted to singularities, and it allows for massive parallelization.

In the seminar, we will study recent space-time methods from the literature.

In case you are interested in the seminar, please contact me via ed* tod *nnob-inu* ta *rentnag* tod *rogerga* tod *b@foo* tod *de.