Correlations in a Posteriori Error Trends for the Finite Element Method in the Presence of Changing Material Parameters

In this letter, we demonstrate that adjoint-based a posteriori elementwise error contribution estimates can be highly correlated in the presence of changing material parameters for finite element method scattering problems. Using a simple lossy dielectric sphere scattering problem set, we explore trends in elementwise a posteriori error contribution estimates as the real permittivity of the spherical scatterer is varied. We show that, not only do elementwise error contribution estimates for this problem remain highly correlated as material parameters vary, but that this correlation is stronger than that apparent for quantities of interest or gradients of such quantities across the same range of dielectric parameters. We also show correlation between the mean and standard deviation of elementwise error contribution estimate magnitudes.

Automated summary

In this study, it was demonstrated that elementwise error contribution estimates remain highly correlated as material parameters change in scattering problems. The correlation between these estimates is shown to be stronger than that for quantities of interest or gradients of such quantities across the same range of dielectric parameters. Additionally, a correlation was found between the mean and standard deviation of elementwise error contribution estimate magnitudes.