This thesis is concerned with the numerical treatment of hyperbolic
conservation laws. These play an important role in describing many
natural phenomena. Challenges in their theoretical as well as numerical
study stem from the fact that spontaneous shock discontinuities can
arise in their solutions, even in finite time and smooth initial states.
Moreover, the numerical treatment of hyperbolic conservations laws
involves many different fields from mathematics, physics, and computer
science. As a consequence, this thesis also provides contributions to
several different fields of research - which are still connected by
numerical conservation laws, however. These contributions include, but
are not limited to, the construction of stable high order quadrature
rules for experimental data, the development of new stable numerical
methods for conservation laws, and the investigation and design of shock
capturing procedures as a means to stabilize high order numerical
methods in the presence of (shock) discontinuities. Jan Glaubitz was
born in Braunschweig, Germany, in 1990 and completed his mathematical
studies (B.Sc., 2014, M.Sc., 2016, Dr. rer. nat., 2019) at TU
Braunschweig. In 2016, he received awards from the German Mathematical
Society (DMV) for his master's thesis as well as from the Society of
Financial and Economic Mathematics of Braunschweig (VBFWM). In 2017, he
was honored with the teaching award "LehrLEO" for the best tutorial at
TU Braunschweig. Since 2020, he holds a position as a postdoctoral
researcher at Dartmouth College, NH, USA.
