Overview on high order schemes for hyperbolic conservation laws

In this first part of the seminar I will give an overview on advanced numerical methods for solving hyperbolic partial differential equations. The presentation will start with a description of the main difficulties connected to these equations and to their wide range of applicability. 

Then, we will recall the most important historical advancements in the development of always more efficient and robust numerical methods. An evidence of each improvement will be given at the aid of simple numerical examples executed directly during the lecture.

 We will close this first part with a focus on high order ADER FV-DG schemes on unstructured fixed and moving meshes, which represent my main contribution to the field and which will be addressed with more details in the second part of the talk.