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

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