A-priori error estimates for hyperbolic balance laws in 1D and hyperbolic approximations of a two-phase flow model in multi-D

This thesis is dedicated to the study of error estimates for approximations of certain nonlinear evolutionary partial differential equations (PDEs) that arise in models for compressible as well as incompressible fluid dynamics. The considered classes of PDEs are either approximated by fully discrete classical discretizations of Finite-Element-type or continuous relaxation models.