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

TL;DR

This paper develops a comprehensive solution theory and variational formulations for general first order systems, providing functional a posteriori error estimates, with applications to electro-magneto-statics and beyond.

Contribution

It introduces a unified functional analysis framework and error estimation techniques for first order systems, including electro-magneto-statics, extending previous methods.

Findings

Established a solution theory for first order systems

Derived variational formulations and error estimates

Applied results to electro-magneto-statics

Abstract

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.