A posteriori error estimates for the Electric Field Integral Equation on polyhedra

TL;DR

This paper develops a residual-based a posteriori error estimate for the Electric Field Integral Equation on polyhedral surfaces, providing computable bounds that aid in numerical analysis and solution accuracy assessment.

Contribution

It introduces a new residual-based error estimator for EFIE on polyhedra, with proven global bounds and practical computability.

Findings

The error estimate is expressed in terms of square-integrable, computable quantities.

Global lower and upper bounds for the error are derived, up to oscillation terms.

The method enhances the accuracy assessment of EFIE solutions on polyhedral geometries.

Abstract

We present a residual-based a posteriori error estimate for the Electric Field Integral Equation (EFIE) on a bounded polyhedron. The EFIE is a variational equation formulated in a negative order Sobolev space on the surface of the polyhedron. We express the estimate in terms of square-integrable and thus computable quantities and derive global lower and upper bounds (up to oscillation terms).