Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient

We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with H\"older continuous coefficient. The obtained convergence rates explicitly depend on the H\"older regularity of the coefficient and the modulus of continuity of the initial data. We compare the theoretically established rates with the experimental rates of a couple of numerical examples

A convergent explicit finite difference scheme for a mechanical model for tumor growth

Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of a mechanical model for tumor growth and the analysis of its dynamics. The system under investigation is given by a multi-phase flow model: The densities of the different cells are governed by a transport equation for the evolution of tumor cells, whereas the velocity field is given by a Brinkman regularization of the classical Darcy's law. An efficient finite difference scheme is proposed and shown to converge to a weak solution of the system. Our approach relies on convergence and compactness arguments in the spirit of Lions (Mathematical Topics in Fluid Dynamics, 1998)

Hanse Law School - A Promising Example of Transnational Legal Education?: An Alumna’s Perspective

Many years after the Bologna declaration a possible reform of the German legal system is still hotly debated. Already 6 years ago the Universities of Bremen, Oldenburg and Groningen introduced a Bachelor/Master programme in European and Comparative Law (Hanse Law School). This contribution shall illustrate in how far these programmes meet new demands of the internationalised labour market. To achieve this the content and the aim of the programmes shall be contrasted with the traditional German legal education and reactions that graduates experienced on the labour market shall be analysed. What can be a promising way for universities to adjust their way of skilling to contemporary challenges? Are the students and graduates of the Hanse Law School, for example, experiencing that the study is “fortiter in re, suaviter in modo” as the slogan advertises and for what kind of career are they equipped

Hanse Law School - A Promising Example of Transnational Legal Education?: An Alumna’s Perspective

Many years after the Bologna declaration a possible reform of the German legal system is still hotly debated. Already 6 years ago the Universities of Bremen, Oldenburg and Groningen introduced a Bachelor/Master programme in European and Comparative Law (Hanse Law School). This contribution shall illustrate in how far these programmes meet new demands of the internationalised labour market. To achieve this the content and the aim of the programmes shall be contrasted with the traditional German legal education and reactions that graduates experienced on the labour market shall be analysed. What can be a promising way for universities to adjust their way of skilling to contemporary challenges? Are the students and graduates of the Hanse Law School, for example, experiencing that the study is “fortiter in re, suaviter in modo” as the slogan advertises and for what kind of career are they equipped

To Share or not to Share (Others' Data) - That is the Question

In her inaugural lecture of 9 June 2023 Prof. Dr. Franziska Weber delved into the conundrum of sharing others’ data: By sharing our personal data we also share – directly and indirectly – information about others. In some situations we are aware of this, in others less so. Weber outlines the social problems this entails with a special focus on negative data externalities. She then illustrates data valuation challenges and presents experimental insights which counter the claim that the sharing individuals are oblivious to the externality they create. She ends with some recommendations on how some fine-tuning of the current legal regime can improve incentives and outcomes on data markets by bringing them more in line with citizens’ preferences. It is striking that the General Data Protection Regulation (GDPR) is tailored to individual data subjects and largely neglects the interdependent notion of data. To improve the GDPR a stronger consideration of the other needs to implemented, be it when consenting, in the context of legitimate interests or other data processing grounds. It is, furthermore, desirable to reduce the processing of allegedly anonymous data which falls outside the scope of the GDPR