A Posteriori Error Estimation of Finite Element Solutions via the Direct Use of Higher Order Hierarchal Test Functions

An a posteriori error estimation of finite element solutions based on the lack of fulfillment of weak formulations is developed and applied to low frequency electromagnetic problems. The error is quantified via higher order hierarchal test functions and local computations of their contributions on the solutions. The method only uses the weak formulation under study with no need of other kind of evaluation.