Estimates for Deviations from Exact Solutions of Maxwell's Initial Boundary Value Problem

TL;DR

This paper develops guaranteed, computable bounds for deviations from exact solutions of Maxwell's initial boundary value problem, enhancing error estimation techniques for hyperbolic PDEs in electromagnetism.

Contribution

It introduces a novel method for deriving guaranteed upper bounds for Maxwell's equations, adapting techniques from wave equation analysis.

Findings

Derived explicit error bounds for Maxwell's equations

Applicable to any admissible vector field in the energy class

Enhances reliability of numerical solutions for electromagnetic problems

Abstract

In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector fields in the space-time cylinder that belongs to the corresponding admissible energy class. For this purpose, we use a method suggested earlier for the wave equation.