Adaptive finite element analysis of 2-D static and steady-state electromagnetic problems

The adaptive finite element methods developed by the authors for a class of 2-D problems in computational electromagnetics are presented. The cases co vered are: magnetostatic, electrostatic, DC conduction and linear AC steady -state eddy currents, both plane and axialsymmetric. Theory is developed in the linear case only, but the resulting methods are applied on a heuristic basis also to non-linear cases and prove able to cope with them. These met hods make use of an element-by-element error estimation and two different h -refinement techniques to adapt meshes made up of first or second-order tri angular elements. Element-by-element error estimation has two main advantag es: it is well suited to cope with the intricate geometries of electromagne tic devices and, at the same time, very cheap from a computational viewpoin t. The local error is estimated by approximately solving a differential pro blem in each element. Theory on which this error estimation method is groun ded is developed in full details and the underlying assumptions are pointed out. The presence in electromagnetic problems of surface currents and inte rfaces between different materials poses new problems in the error estimati on with respect to other applications in which similar methods are used The h-refinement technique can be selected between the bisection method and th e centroid method followed by a Delaunay step. Accuracy and efficiency of t he proposed method is discussed on the basis of previous work of the author s and further numerical experiments. Applications to realistic models showi ng good performances of the proposed methods are reported. Copyright (C) 19 99 John Wiley & Sons, Ltd.