Functional derivatives and optimal discretization based refinement criteria for adaptive finite element analysis with scalar tetrahedra

Efficient functional derivative formulae suitable for optimal discretization based refinement criteria are developed for EM field 3-D adaptive finite element analysis (FEA) with scalar tetrahedra. Results for generalized scalar Poisson and Helmholtz systems are derived directly from first principles, and confirmed numerically through fundamental benchmark evaluations. Practical adaption applications are illustrated for selected FEA refinement models.