Solution Theory, Variational Formulations, and Functional A Posteriori Error Estimates for General First Order Systems with Applications to Electro-Magneto-Statics and More

We prove a comprehensive solution theory using tools from functional analysis, show corresponding variational formulations, and present functional a posteriori error estimates for general linear first order systems. As a prototypical application we will discuss the system of electro-magneto statics with mixed tangential and normal boundary conditions. Second order systems will be considered as well.