Volume III is divided into 28 chapters, the first of which focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This section presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It also includes examples of advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a revised perspective on the analysis of well-known time-stepping methods. Additionally, the concluding chapters on hyperbolic equations argue for the application of continuous finite elements in solving this class of problems, which have previously been overlooked in favor of finite volumes approaches. weiterlesen