Exploring Bounds in Complementary Formulations for Electroquasistatics

It is well established that complementary formulations for static electromagnetic problems yield upper and lower energy bounds, a result that has been demonstrated only numerically for magnetoquasistatic (MQS) problems. However, this aspect remains completely unexplored for electroquasistatic (EQS) problems. The primary objective of this article is to solve an EQS problem for the first time using two complementary formulations. The secondary aim is to address the existing gap in the literature by numerically investigating whether energy bounds exist for EQS problems, following the approach previously applied to MQS problems.