arXiv subjects

Dirk Pauly

Publications and source records attributed to Dirk Pauly.

58 records · Page 4Linked to original sources

arXiv2011

On the Polynomial and Exponential Decay of Eigen-Forms of Generalized Time-Harmonic Maxwell Problems

We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. As a canonical application we show that the corresponding eigen-values do not accumulate in R \ {0} and that by means of Eidus' limiting absorption principle a Fredholm alternative holds true.

math.AP↗

arXiv2011

Two-Sided A Posteriori Error Bounds for Electro-Magneto Static Problems

This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based upon purely functional argumentation and does not attract specific properties of an approximation method. Therefore, the estimates derived in the paper at hand are applicable to any approximate solution that belongs to the corresponding energy space. Such estimates (also called error majorants of the functional type) have been derived earlier for elliptic problems.

math.AP↗

arXiv2011

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

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.

math.AP↗

arXiv2011

Hodge-Helmholtz Decompositions of Weighted Sobolev Spaces in Irregular Exterior Domains with Inhomogeneous and Anisotropic Media

We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, in electro-magnetic theory for exterior domains. In the appendix we translate our results to the classical framework of vector analysis.

math.AP↗