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

2011/05/20 by Dirk Pauly, Pauly, Dirk, Sergey Repin +3
Engineering · Mathematics · #35 L 15 #65 N 15 #78 M 30 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1105.4110

openalex publication_date 2011/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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