# Dimitrios Zacharenakis, M. Sc.

Department Mathematics

Numerical Analysis

Work
Dolivostraße 15

64293
Darmstadt

Office: S4|10 201

work +49 6151 16-23197

zacharenakis@mathematik.tu-...

## Working area(s)

My **Researchgate** profile

# CV

University Education
| ||

2012 | BSc at University of Crete in Applied Mathematics | |

2015 | MSc at National Technical University of Athens in Mathematical Modeling in Modern Technologies | |

2015 – 2018 | PhD student at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart | |

2018 | Visiting scholar (as part of PhD project) in University of Maryland, College Park | |

2018 – | Continue as PhD student at University of Darmstadt |

# Research Interest

- Conservation Laws
- Discontinuous Galerkin Methods
- Error estimates
- Two phase flows

My research interests lie in partial differential equations and their numerical approximation. To begin, I consider conservation laws and in particular systems that are labeled as hyperbolic-elliptic. In brief, this stems from the fact that the considered systems describe the dynamics of a liquid-vapor mixture which undergoes phase transitions.

In order to understand the properties of such systems, I investigate how they can be approximated using a discontinuous Galerkin method. In fact, using an a posteriori error analysis, I examine the difference between exact and numerical solutions. The mathematical tools that I employ, include a variant of the relative entropy technique, which is used for stability analysis of hyperbolic conservation laws, and estimates from elliptic problems. To apply such techniques, one has to study the properties of solutions of hyperbolic conservation laws. The motivation arises from the fact that smooth solutions of these systems break down in finite time even for smooth initial data. Thus, different classes of solutions, e.g. entropy solutions, are meaningful to consider. Similarly, in hyperbolic-elliptic systems, such as the Euler-Korteweg (EK) equations, weak entropic-strong uniqueness theorems and stability of solutions are important notions for my research.

Moreover, including a viscosity term to the EK system, gives rise to the Navier-Stokes-Korteweg equations (NSK). In this case, I examine the behavior of these systems from a theoretical and a numerical point of view.